Question

If 9x+1/x=10 find the value of 81x2+y2

Answer 1

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Answer 2

Your question is incorrect. May be the correct question is, If 9x+$\frac{1}{x}$ = 10, find the value of 81x² + $\frac{1}{x^{2} }$.

The value of 81x² + $\frac{1} x^{2}$ = 82

Given that 9x + $\frac{1}{x}$ = 10

To find, value of 81x² + $\frac{1}x^{2}$

Solution:-

9x + $\frac{1}{x}$ = 10

Squaring both the sides of equation, we get:

(9x + $\frac{1}{x}$)² = (10)²

⇒ (9x)²+($\frac{1}{x}$)² = (10)²      ∵ a²+b²= a²+b²+2ab

⇒ 81x²+ $\frac{1}{x^{2} }$+ 2× 9x × $\frac{1}{x}$ = 100 ( a= 9x and b= $\frac{1}{x}$)

⇒ 81x²+ $\frac{1}{x^{2} }$= 100-18

⇒ 81x²+ $\frac{1}{x^{2} }$= 82

Hence, the value of 81x² + $\frac{1}{x^{2} }$ is 82.

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