Question

If x - 1/x = 9 then evaulate x² + 1/x²

Answer 1

Answer:

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Answer 2

Question

If $x-\frac{1}{x}=9$ . To Find $x^2+\frac{1}{x^2}$

Given:

$x-\frac{1}{x}=9$

To Find:

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

Solution:

$x-\frac{1}{x}=9$

$\textsf{squaring on both sides}$

$x-\frac{1}{x}=9\\\\(x-\frac{1}{x})^2=9^2\\\\(a-b)^2=a^2-b^2-2ab=81\\\\(x-\frac{1}{x})^2=x^2-\frac{1}{2}^2-2\times x \:\times\frac{1}{x}=81\\\\x^2+\frac{1}{x^2}-2=81\\\\x^2+\frac{1}{x^2}=81-2\\\\x^2+\frac{1}{x^2}=81+2\\\\x^2+\frac{1}{x^2}=83\\\\\boxed{x^2+\frac{1}{x^2}=83}$

Answer:

$\boxed{x^2+\frac{1}{x^2}=83}$