Question

If x+1/x=5 find the value of x⁴+1/x⁴.​

Answer 1

Step-by-step explanation:

⇒ x + 1/x = 5

           Square on both sides:

⇒ (x + 1/x)^2 = 5^2

            (a + b)^2 = a^2 + b^2 + 2ab

⇒ x^2 + (1/x)^2 + 2(x*1/x) = 25

⇒ x^2 + 1/x^2 + 2 = 25

⇒ x^2 + 1/x^2 = 23

          Square on both sides:

⇒ (x^2 + 1/x^2)^2 = 23^2

⇒ x^4 + 1/x^4 + 2 = 529

⇒ x^4 + 1/x^4 = 527

Answer 2

Given :-

$\to\sf If \: x + \frac{1}{x} = 5$

To Find :-

$\to\sf The \: value \: of \: x^{4} + \frac{1}{x^{4}}$

Solution :-

$:\implies\sf x + \frac{1}{x} = 5$

$:\implies\sf (x + \frac{1}{x})^{2} = 5^{2} \: \: [\bf Squaring \: on \: both \: sides ]</p><p>$

By using this identity,

• (a + b)² = a² + b² + 2ab

$:\implies\sf x^{2} + (\frac{1}{x})^{2} + 2(x \times\frac{1}{x}) = 25$

$:\implies\sf x^{2} + \frac{1}{x^{2}} + 2 = 25$

$:\implies\sf x^{2} + \frac{1}{x^{2}} = 25 - 2$

$:\implies\sf x^{2} + \frac{1}{x^{2}} = 23$

$:\implies\sf (x^{2} + \frac{1}{x^{2}})^{2} = 23^{2} \: \: [ \bf Squaring \: on \: both \: sides ]$

$:\implies\sf x^{4} + \frac{1}{x^{4}} + 2 = 529$

$:\implies\sf x^{4} + \frac{1}{x^{4}} = 529 - 2$

$:\implies\underline{\boxed{\blue{\sf x^{4} + \frac{1}{x^{4}} = 527}}}$