{"id":27925,"date":"2022-02-17T18:59:45","date_gmt":"2022-02-17T13:29:45","guid":{"rendered":"https:\/\/apboardsolutions.guru\/?p=27925"},"modified":"2022-02-17T18:59:45","modified_gmt":"2022-02-17T13:29:45","slug":"ap-board-8th-class-maths-solutions-chapter-12-ex-12-4-in-telugu","status":"publish","type":"post","link":"https:\/\/apboardsolutions.guru\/ap-board-8th-class-maths-solutions-chapter-12-ex-12-4-in-telugu\/","title":{"rendered":"AP Board 8th Class Maths Solutions Chapter 12 \u0c15\u0c3e\u0c30\u0c23\u0c3e\u0c02\u0c15 \u0c35\u0c3f\u0c2d\u0c1c\u0c28 Ex 12.4"},"content":{"rendered":"

AP SCERT 8th Class Maths Textbook Solutions<\/a> Chapter 12 \u0c15\u0c3e\u0c30\u0c23\u0c3e\u0c02\u0c15 \u0c35\u0c3f\u0c2d\u0c1c\u0c28 Ex 12.4 Textbook Exercise Questions and Answers.<\/p>\n

AP State Syllabus 8th Class Maths Solutions 12th Lesson \u0c15\u0c3e\u0c30\u0c23\u0c3e\u0c02\u0c15 \u0c35\u0c3f\u0c2d\u0c1c\u0c28 Exercise 12.4<\/h2>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 1.
\n\u0c08 \u0c15\u0c4d\u0c30\u0c3f\u0c02\u0c26\u0c3f \u0c35\u0c3e\u0c15\u0c4d\u0c2f\u0c2e\u0c41\u0c32\u0c32\u0c4b \u0c38\u0c30\u0c3f\u0c2f\u0c48\u0c28 \u0c35\u0c3e\u0c15\u0c4d\u0c2f\u0c2e\u0c41\u0c28\u0c41 \u0c17\u0c41\u0c30\u0c4d\u0c24\u0c3f\u0c02\u0c2a\u0c41\u0c2e\u0c41.
\n\u0c38\u0c3e\u0c27\u0c28.
\n(i) 3(x – 9) = 3x – 9
\n\u21d2 3x – 3 \u00d7 9 = 3x – 9
\n\u21d2 3x – 27 = 3x – 9
\n– 27 \u2260 – 9
\n\u2234 \u0c07\u0c1a\u0c4d\u0c1a\u0c3f\u0c28 \u0c17\u0c23\u0c3f\u0c24 \u0c35\u0c3e\u0c15\u0c4d\u0c2f\u0c02 \u0c38\u0c30\u0c3f\u0c2f\u0c48\u0c28\u0c26\u0c3f \u0c15\u0c3e\u0c26\u0c41.<\/p>\n

(ii) x(3x + 2) = 3x2<\/sup> + 2
\n\u21d2 x \u00d7 3x + x \u00d7 2 = 3x2<\/sup> + 2
\n\u21d2 3x2<\/sup> + 2x \u2260 3x2<\/sup> + 2
\n\u2234 \u0c07\u0c1a\u0c4d\u0c1a\u0c3f\u0c28 \u0c17\u0c23\u0c3f\u0c24 \u0c35\u0c3e\u0c15\u0c4d\u0c2f\u0c02 \u0c38\u0c30\u0c3f\u0c2f\u0c48\u0c28\u0c26\u0c3f \u0c15\u0c3e\u0c26\u0c41.<\/p>\n

(iii) 2x + 3x = 5x2<\/sup>
\n\u21d2 5x = 5x2<\/sup>
\n\u21d2 x \u2260 x2<\/sup>
\n\u2234 \u0c07\u0c1a\u0c4d\u0c1a\u0c3f\u0c28 \u0c17\u0c23\u0c3f\u0c24 \u0c35\u0c3e\u0c15\u0c4d\u0c2f\u0c02 \u0c38\u0c30\u0c3f\u0c2f\u0c48\u0c28\u0c26\u0c3f \u0c15\u0c3e\u0c26\u0c41.<\/p>\n

(iv) 2x + x + 3x = 5x
\n\u21d2 6x = 5x
\n\u21d2 6 \u2260 5
\n\u2234 \u0c07\u0c1a\u0c4d\u0c1a\u0c3f\u0c28 \u0c17\u0c23\u0c3f\u0c24 \u0c35\u0c3e\u0c15\u0c4d\u0c2f\u0c02 \u0c38\u0c30\u0c3f\u0c2f\u0c48\u0c28\u0c26\u0c3f \u0c15\u0c3e\u0c26\u0c41.<\/p>\n

(v) 4p+ 3p + 2p + p – 9p = 0
\n4p + 3p + 2p + p – 9p = 0
\n10p – 9p = 0
\np = 0
\n\u2234 \u0c07\u0c26\u0c3f \u0c05\u0c38\u0c02\u0c2d\u0c35\u0c02
\n\u2234 \u0c07\u0c1a\u0c4d\u0c1a\u0c3f\u0c28 \u0c17\u0c23\u0c3f\u0c24 \u0c35\u0c3e\u0c15\u0c4d\u0c2f\u0c02 \u0c38\u0c30\u0c3f\u0c2f\u0c48\u0c28\u0c26\u0c3f \u0c15\u0c3e\u0c26\u0c41.<\/p>\n

(vi) 3x + 2y = 6xy
\na + b \u2260 ab \u0c2a\u0c4d\u0c30\u0c15\u0c3e\u0c30\u0c02 \u0c2a\u0c48 \u0c17\u0c23\u0c3f\u0c24 \u0c35\u0c3e\u0c15\u0c4d\u0c2f\u0c02 \u0c38\u0c30\u0c3f\u0c2f\u0c48\u0c28\u0c26\u0c3f \u0c15\u0c3e\u0c26\u0c41.<\/p>\n

(vii) (3x)2<\/sup> + 4x +7 = 3x2<\/sup> + 4x + 7
\n\u21d2 (3x) = 3x
\n\u21d2 9x = 3x
\n\u21d2 9 = 3 \u0c07\u0c26\u0c3f \u0c05\u0c38\u0c02\u0c2d\u0c35\u0c02
\n\u2234 \u0c07\u0c1a\u0c4d\u0c1a\u0c3f\u0c28 \u0c17\u0c23\u0c3f\u0c24 \u0c35\u0c3e\u0c15\u0c4d\u0c2f\u0c02 \u0c38\u0c30\u0c3f\u0c2f\u0c48\u0c28\u0c26\u0c3f \u0c15\u0c3e\u0c26\u0c41.<\/p>\n

(viii) (2x)2<\/sup> + 5x = 4x + 5x = 9x
\n\u21d2 4x2<\/sup> + 5x = 4x + 5x
\n\u21d2 4x2<\/sup> = 4x
\n\u21d2 x2<\/sup> = x
\n\u21d2 x = \\(\\sqrt{\\mathrm{x}}\\) \u0c07\u0c26\u0c3f \u0c05\u0c38\u0c02\u0c2d\u0c35\u0c02
\n\u2234 \u0c07\u0c1a\u0c4d\u0c1a\u0c3f\u0c28 \u0c17\u0c23\u0c3f\u0c24 \u0c35\u0c3e\u0c15\u0c4d\u0c2f\u0c02 \u0c38\u0c30\u0c3f\u0c2f\u0c48\u0c28\u0c26\u0c3f \u0c15\u0c3e\u0c26\u0c41.<\/p>\n

(ix) (2a + 3)2<\/sup> = 2a2<\/sup> + 6a + 9
\n\u21d2 (2a)2<\/sup> + 2 \u00d7 2a \u00d7 3 + 32<\/sup> = 2a2<\/sup> + 6a + 9
\n\u21d2 4a2<\/sup> + 12a + 9 = 2a2<\/sup> + 6a + 9
\n\u21d2 4a2<\/sup> + 12a = 2a2<\/sup> + 6a
\n\u21d2 2a2<\/sup> + 6a \u2260 a2<\/sup> + 3a.
\n\u0c15\u0c3e\u0c35\u0c41\u0c28\u0c3e \u0c07\u0c1a\u0c4d\u0c1a\u0c3f\u0c28 \u0c17\u0c23\u0c3f\u0c24 \u0c35\u0c3e\u0c15\u0c4d\u0c2f\u0c02 \u0c38\u0c30\u0c3f\u0c2f\u0c48\u0c28\u0c26\u0c3f \u0c15\u0c3e\u0c26\u0c41.<\/p>\n

(x) x = – 3 \u0c2a\u0c4d\u0c30\u0c24\u0c3f\u0c15\u0c4d\u0c37\u0c47\u0c2a\u0c3f\u0c02\u0c1a\u0c41\u0c2e\u0c41.<\/p>\n

(a) x2<\/sup> + 7x + 12 = (-3)2<\/sup> +7 (-3) + 12
\n= 9 + 4 + 12 = 25
\nx2<\/sup> + 7x + 12 = (-3)2<\/sup> + 7 (-3) + 12
\n= 9 – 21 + 12
\n= 21 – 21 = 0
\n= 0 \u2260 25 (\u0c05\u0c38\u0c24\u0c4d\u0c2f\u0c02 )<\/p>\n

(b) x2<\/sup> – 5x + 6 = (-3)2<\/sup> – 5(- 3) + 6
\n= 9 – 15 + 6 = 0
\nx2<\/sup> – 5x + 6 = (-3)2<\/sup> – 5 (-3) – 6
\n= 9 + 15 + 6
\n= 30 \u2260 0(\u0c05\u0c38\u0c24\u0c4d\u0c2f\u0c02)<\/p>\n

(c) x2<\/sup> + 5x = (-3)2<\/sup> + 5 (-3) + 6
\n= – 9 – 15 = – 24
\nx2<\/sup> + 5x = (-3)2<\/sup> + 5 (-3)
\n= 9 – 15 = – 6 \u2260 – 24 (\u0c05\u0c38\u0c24\u0c4d\u0c2f\u0c02)<\/p>\n

(xi) (x – 4)2<\/sup> = x2<\/sup> – 16
\n(x – 4)2<\/sup> = (x)2<\/sup> – (4)2<\/sup>
\n(a – b)2<\/sup> \u2260 a2<\/sup> – b2<\/sup> (\u0c32\u0c47\u0c26\u0c3e)
\n\u21d2 x2<\/sup> – 2 \u00d7 x \u00d7 4 + 42<\/sup> = x2<\/sup> – 16
\n\u21d2 x2<\/sup> – 8x + 16 = x2<\/sup> – 16
\n\u21d2 – 8x = 0
\n\u21d2 x = 0
\n\u0c07\u0c26\u0c3f \u0c05\u0c38\u0c02\u0c2d\u0c35\u0c02. \u0c15\u0c3e\u0c35\u0c41\u0c28 \u0c07\u0c1a\u0c4d\u0c1a\u0c3f\u0c28 \u0c17\u0c23\u0c3f\u0c24 \u0c35\u0c3e\u0c15\u0c4d\u0c2f\u0c02 \u0c38\u0c30\u0c3f\u0c2f\u0c48\u0c28\u0c26\u0c3f \u0c15\u0c3e\u0c26\u0c41.<\/p>\n

(xii) (x + 7)2<\/sup> = x2<\/sup> + 49
\n(x + 7)2<\/sup> = x2<\/sup> + 49 = (x)2<\/sup> + (7)2<\/sup>
\n(a + b)2<\/sup> \u2260 a2<\/sup> + b2<\/sup>
\n\u2234 (x + 7)2<\/sup> \u2260 (x)2<\/sup> + (7)2<\/sup>
\n\u2234 \u0c07\u0c26\u0c3f \u0c05\u0c38\u0c24\u0c4d\u0c2f \u0c17\u0c23\u0c3f\u0c24 \u0c2a\u0c4d\u0c30\u0c35\u0c1a\u0c28\u0c02.<\/p>\n

(xiii) (3a + 4b) (a – b) = 3a2<\/sup> – 4a2<\/sup>
\n3a (a – b) + 4b (a – b) = 3a2<\/sup> – 4a2<\/sup>
\n3a2<\/sup> – 3ab + 4ab – 4b2<\/sup> = – a2<\/sup>
\nab – 4b2<\/sup> + 4a2<\/sup> = 0
\n\u21d2 \u0c07\u0c26\u0c3f \u0c05\u0c38\u0c02\u0c2d\u0c35\u0c02. \u0c15\u0c3e\u0c35\u0c41\u0c28 \u0c07\u0c1a\u0c4d\u0c1a\u0c3f\u0c28 \u0c17\u0c23\u0c3f\u0c24 \u0c35\u0c3e\u0c15\u0c4d\u0c2f\u0c02 \u0c05\u0c38\u0c24\u0c4d\u0c2f\u0c02.<\/p>\n

(xiv) (x + 4) (x + 2) = x2<\/sup> + 8
\n\u21d2 x2<\/sup> + 6x + 8 = x2<\/sup> + 8
\n\u21d2 6x = 0
\n\u2234 x = 0
\n\u0c07\u0c26\u0c3f \u0c05\u0c38\u0c02\u0c2d\u0c35\u0c02. \u0c15\u0c3e\u0c35\u0c41\u0c28 \u0c07\u0c1a\u0c4d\u0c1a\u0c3f\u0c28 \u0c17\u0c23\u0c3f\u0c24 \u0c35\u0c3e\u0c15\u0c4d\u0c2f\u0c02 \u0c05\u0c38\u0c24\u0c4d\u0c2f\u0c02.<\/p>\n

(xv) (x – 4) (x – 2) = x2<\/sup> – 8
\n\u21d2 x2<\/sup> – 6x + 8 = x2<\/sup> – 8
\nRHS \u0c32\u0c4b (-6x) \u0c2a\u0c26\u0c02 \u0c32\u0c4b\u0c2a\u0c3f\u0c02\u0c1a\u0c3f\u0c28\u0c26\u0c3f \u0c15\u0c3e\u0c35\u0c41\u0c28 \u0c07\u0c1a\u0c4d\u0c1a\u0c3f\u0c28 \u0c17\u0c23\u0c3f\u0c24 \u0c35\u0c3e\u0c15\u0c4d\u0c2f\u0c02 \u0c05\u0c38\u0c24\u0c4d\u0c2f\u0c02.<\/p>\n

(xvi) 5x3<\/sup> \u00f7 5x3<\/sup> = 0
\n\\(\\frac {5x}{5x}\\) = 0
\n\u21d2 x3-3<\/sup> = 0 \u21d2 x0<\/sup> = 1 (\u2235 \u0c15\u0c3e\u0c28\u0c3f x0<\/sup> = 1)
\n\u2234 1 \u2260 0
\n\u0c07\u0c26\u0c3f \u0c05\u0c38\u0c02\u0c2d\u0c35\u0c02. \u0c15\u0c3e\u0c35\u0c41\u0c28 \u0c07\u0c1a\u0c4d\u0c1a\u0c3f\u0c28 \u0c17\u0c23\u0c3f\u0c24 \u0c35\u0c3e\u0c15\u0c4d\u0c2f\u0c02 \u0c05\u0c38\u0c24\u0c4d\u0c2f\u0c02 .<\/p>\n

(xvii) 2x3<\/sup> + 1 \u00f7 2x3<\/sup> = 1
\n\u21d2 \\(\\frac{2 x^{3}+1}{2 x^{3}}\\) = 1
\n\u0c39\u0c3e\u0c30\u0c02\u0c32\u0c4b (+1) \u0c2a\u0c26\u0c02 \u0c32\u0c4b\u0c2a\u0c3f\u0c02\u0c1a\u0c3f\u0c28\u0c26\u0c3f \u0c15\u0c3e\u0c35\u0c41\u0c28 \u0c07\u0c1a\u0c4d\u0c1a\u0c3f\u0c28 \u0c17\u0c23\u0c3f\u0c24 \u0c35\u0c3e\u0c15\u0c4d\u0c2f\u0c02 \u0c05\u0c38\u0c24\u0c4d\u0c2f\u0c02.<\/p>\n

(xviii) 3x + 2 \u00f7 3x = \\(\\frac{2}{3 x}\\)
\n\u21d2 \\(\\frac{3 x+2}{3 x}=\\frac{2}{3 x}\\)
\n\u21d2 \\(\\frac{3 x}{3 x}+\\frac{2}{3 x}=\\frac{2}{3 x}\\)
\n\u21d2 1 + \\(\\frac{2}{3 x}=\\frac{2}{3 x}\\)
\n\u21d2 1 = 0
\n\u0c07\u0c26\u0c3f \u0c05\u0c38\u0c02\u0c2d\u0c35\u0c02. \u0c15\u0c3e\u0c35\u0c41\u0c28 \u0c07\u0c1a\u0c4d\u0c1a\u0c3f\u0c28 \u0c17\u0c23\u0c3f\u0c24 \u0c35\u0c3e\u0c15\u0c4d\u0c2f\u0c02 \u0c05\u0c38\u0c24\u0c4d\u0c2f\u0c02.<\/p>\n

(xix) 3x + 5 \u00f7 3 = 5
\n\u21d2 \\(\\frac{3 x+5}{3}\\) = 5
\n\u21d2 \\(\\frac{3 x}{3}+\\frac{5}{3}\\) = 5
\n\u21d2 x + \\(\\frac{5}{3}\\) = 5
\n\u2234 RHS \u0c32\u0c4b (x) \u0c2a\u0c26\u0c02 \u0c32\u0c4b\u0c2a\u0c3f\u0c02\u0c1a\u0c3f\u0c28\u0c26\u0c3f \u0c15\u0c3e\u0c35\u0c41\u0c28 \u0c07\u0c26\u0c3f \u0c05\u0c38\u0c24\u0c4d\u0c2f\u0c02.<\/p>\n

(xx) \\(\\frac{4 x+3}{3}\\) = x + 1
\n\u21d2 \\(\\frac{4 \\mathrm{x}}{3}+\\frac{3}{3}\\) = x + 1
\n\u21d2 \\(\\frac{4x}{3}\\) + 1 = x + 1
\n\u0c07\u0c26\u0c3f \u0c05\u0c38\u0c24\u0c4d\u0c2f\u0c02.<\/p>\n","protected":false},"excerpt":{"rendered":"

AP SCERT 8th Class Maths Textbook Solutions Chapter 12 \u0c15\u0c3e\u0c30\u0c23\u0c3e\u0c02\u0c15 \u0c35\u0c3f\u0c2d\u0c1c\u0c28 Ex 12.4 Textbook Exercise Questions and Answers. AP State Syllabus 8th Class Maths Solutions 12th Lesson \u0c15\u0c3e\u0c30\u0c23\u0c3e\u0c02\u0c15 \u0c35\u0c3f\u0c2d\u0c1c\u0c28 Exercise 12.4 \u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 1. \u0c08 \u0c15\u0c4d\u0c30\u0c3f\u0c02\u0c26\u0c3f \u0c35\u0c3e\u0c15\u0c4d\u0c2f\u0c2e\u0c41\u0c32\u0c32\u0c4b \u0c38\u0c30\u0c3f\u0c2f\u0c48\u0c28 \u0c35\u0c3e\u0c15\u0c4d\u0c2f\u0c2e\u0c41\u0c28\u0c41 \u0c17\u0c41\u0c30\u0c4d\u0c24\u0c3f\u0c02\u0c2a\u0c41\u0c2e\u0c41. \u0c38\u0c3e\u0c27\u0c28. (i) 3(x – 9) = 3x – 9 \u21d2 3x – 3 \u00d7 9 = …<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[6],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/posts\/27925"}],"collection":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/comments?post=27925"}],"version-history":[{"count":1,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/posts\/27925\/revisions"}],"predecessor-version":[{"id":27926,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/posts\/27925\/revisions\/27926"}],"wp:attachment":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/media?parent=27925"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/categories?post=27925"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/tags?post=27925"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}