Question

Weckshet
Mathematics.
1. If x+1/x= 4, then find the value of x²+1/x²​

Answer 1

EXPLANATION.

⇒ (x + 1/x) = 4.

As we know that,

Squaring on both sides of the equation, we get.

⇒ (x + 1/x)² = (4)².

⇒ x² + 1/x² + 2(x)(1/x) = 16.

⇒ x² + 1/x² + 2 = 16.

⇒ x² + 1/x² = 16 - 2.

⇒ x² + 1/x² = 14.

Answer 2

$\huge \sf\red{ {x}^{2} + \frac{1}{ {x}^{2} } = 14}$

Step-by-step explanation:

$x + \frac{1}{x} = 4 \\ \\ = > {(x + \frac{1}{x} )}^{2} = ( {4)}^{2} ..(squaring \: both \: sides) \\ \\ = > {x}^{2} + 2( \cancel{x })( \frac{1}{ \cancel{x} }) + (\frac{1}{ { x} } {)}^{2} = 16 \\ \\ \{by \: the \: formula \: ( {a + b)}^{2} = {a}^{2} + 2ab + {b}^{2} \} \\ = > {x}^{2} + \frac{1}{ {x}^{2} } + 2 = 16 \\ \\ = > {x}^{2} + \frac{1}{ {x}^{2} } = 16 - 2 \\ \\ \red{ {x}^{2} + \frac{1}{ {x}^{2} } = 14}$

Hence the value of x² + 1/x² = 14.

hope it helps.