Question

If x + 1/x = 8 , find the value of x² + 1/x²

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Answer 1

Given :

$\sf \: x + \dfrac{1}{x} = 8$

To Find :

$\sf \: {x}^{2} + \dfrac{1}{ {x}^{2} }$

Solution :

$\longrightarrow \sf \: x + \dfrac{1}{x} = 8$

Squaring both the sides

$\longrightarrow \sf \: (x + \dfrac{1}{x})^{2} = ( {8})^{2}$

$\longrightarrow \sf \: {x}^{2} + 2(x)( \dfrac{1}{x} ) + (\dfrac{1}{x} )^{2} = 64$

$\longrightarrow \sf \: ({x})^{2} + 2(x)( \dfrac{1}{x} ) + (\dfrac{1}{x} )^{2} = 64$

$\longrightarrow \sf \: {x}^{2} + 2 + \dfrac{1}{ {x}^{2} } = 64$

$\longrightarrow \sf \: {x}^{2} + \dfrac{1}{ {x}^{2} } = 64 - 2$

$\longrightarrow \boxed{ \sf \: {x}^{2} + \dfrac{1}{ {x}^{2} } = 62}$

Answer 2

Answer:

62 is the correct answer

Step-by-step explanation:

hopes it helps you