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if 3x+1/3x = 3, find : (i) 9x^2+1/9x^2​

Answer 1

Answer:

18

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If 3x + (1/3x) = 3; find : 9x2 + (1/9x2)

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asked May 20, 2019 in Class VIII Maths by navnit40 Expert (40.4k points)

If 3x + (1/3x) = 3; find : (i) 9x2 + (1/9x2)

(ii) 27x3 + (1/27x3)

algebraic identities

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answered May 20, 2019 by muskan15 Expert (37.9k points)

(i) 3x + (1/3x) = 3

⇒ (3x + (1/3x))2 = (3)2

⇒ (3x)2 + (1/3x)2 + 2 × 3x × (1/3x )= 9

⇒ 9x2 + (1/9x2) + 2 = 9 ⇒ 9x2 + (1/9x2) = 9 -2

⇒ 9x2 + (1/9x2 ) = 7

(ii) 3x + (1/3x) = 3

⇒ (3x + (1/3x))3 = (3)3

⇒ (3x)3 + (1/3x)3 + 3 × 3x × (1/3x) (3x + 1/3x) = 27

⇒ 27x3 + (1/27x3) + 3(3x + (1/2x)) = 27

⇒ 27x3 + (1/27x3) + 3(3) = 27

⇒ 27x3 + (1/27x3) = 27 -9

⇒ 27x3 + (1/27x3) = 18