Question

If (x + 1/x)= 2 , then the value of (x^6 + 1/x^6) is: ?​

Answer 1

Answer:

$\huge\bf\underline\red{AnSweR:}$

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

$( {x + \frac{1}{x} })^{2} = 4$

${x}^{2} + \frac{1}{ {x}^{2} } + 2 = 4$

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

$( { {x }^{2} + \frac{1}{ {x}^{2} } })^{3} = 8$

${x}^{6} + \frac{1}{ {x}^{6} } + 3( {x})^{2} ( \frac{1}{ {x}^{2} })( {x}^{2} + \frac{1}{ {x}^{2} } ) = 8$

${x}^{6} + \frac{1}{ {x}^{6} } = 8 - 3 \times 2$

$\implies\bf\blue{2}$

Answer 2

$\huge\boxed{\fcolorbox{red}{pink}{Your's Answer}}$

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

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

${x}^{2} + { \frac{1}{ {x}^{2} } + 2 = 4$

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

$( { {x}^{2} + \frac{1}{ {x}^{2} } })^{3} = 8$

${x}^{6} + \frac{1}{ {x}^{6} } = 8 - 3 \times 2$

${x}^{6} + \frac{1}{ {x}^{6} } = 10$

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