Question

If x-1/x=9, find the value of x²+ 1/x²​

Answer 1

Answer:

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

Step-by-step explanation:

$x - \frac{1}{x} = 9 \\ squring \: on \: both \: the \: sides \\ {(x - \frac{1}{x} )}^{2} = {(9)}^{2} \\ {(x)}^{2} + {( \frac{1}{x} )}^{2} - 2(x)( \frac{1}{x} ) = 81 \\ {x}^{2} + \frac{1}{ {x}^{2} } - 2 = 81 \\ {x}^{2} + \frac{1}{ {x}^{2} } = 81 + 2 \\ {x}^{2} + \frac{1}{ {x}^{2} } = 83$

Answer 2

Given : x - 1/x  = 9

To Find : Value of  x⁴  + 1/x⁴

Solution:

x - 1/x  = 9

Squaring both sides

(x  - 1/x)² = 9²

Using identity (a - b)² = a² + b² - 2ab

a = x  and b = 1/x

=> x² + 1/x²  - 2x(1/x) = 81

=> x² + 1/x² - 2 = 81

=> x² + 1/x² = 81 + 2

=> x² + 1/x² = 83

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