If 3x-13x -3- then find 9x2-19x2-

3x+13x = 3 Squaring on both sides ⇒ 9x^2+2× 3x×13x+19x^2 = 9 ⇒ 9x^2+19x^2+2 = 9 ∴ 9x^2+19x^2 = 7 #160; ...

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(a + b)^2 Expansion and Visualisation

If 3x+13x =...

Question

If $3 x + \frac{1}{3 x} = 3$ , then find $9 x^{2} + \frac{1}{9 x^{2}}$ .

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Solution

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3 x + \frac{1}{3 x} = 3

9 x^{2} + \frac{1}{9 x^{2}}

3 x - \frac{1}{3 x} = 5

9 x^{2} + \frac{1}{9 x^{2}}

9 x^{2} + \frac{1}{9 x^{2}}

(3 x + \frac{1}{3 x}) = \frac{8}{3}

3 x - \frac{1}{3 x} = 15

9 x^{2} + \frac{1}{9 x^{2}}

If $3 x - \frac{1}{3 x} = 5$ , find :

(i) $9 x^{2} + \frac{1}{9 x^{2}}$

(ii) $81 x^{4} + \frac{1}{81 x^{4}}$

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