Question

IF x+1/x=4 then find x2+1/x2

Answer 1

x + 1)/x =4

x + 1 = 4x

1 = 4x - x

3x = 1

x = 1/3

(x² + 1)/x²

1/9 + 1)/x²

1 + 9)/9]/x²

10/9=x²

9x² = 10

3x = \/10

3x = \/10/3

Answer 2

Answer:

$Using \: \: the \: \: identity : \\ {(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab$

Step-by-step explanation:

$x + \frac{1}{x} = 4 \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } = \: ?? \\ {x}^{2} + { (\frac{1}{x}) }^{2} = {4}^{2} \\ {x}^{2} + { (\frac{1}{x} )}^{2} = 16 \\ {x}^{2} + \frac{1}{ {x}^{2} } + (2 \times \cancel x \times \frac{1}{ \cancel x} ) = 16 \\ {x}^{2} + \frac{1}{ {x}^{2} } + 2 = 16 \\ {x}^{2} + \frac{1}{ {x}^{2} } = 16 - 2 \\ \boxed{ \large {x + \frac{1}{ {x}^{2} } = \underline{ \underline{ 14}}}}$