Question

if x + 1/x=5 , find the value of x^4 + 1/x^4

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Answer 1

Step-by-step explanation:

hope this answer will help uuuu

Answer 2

Given:

$\sf \: x + \dfrac{1}{x} = 5$

To find:

$\sf{} {x}^{4} + \dfrac{1}{ {x}^{4} }$

Solution:

$\sf \: x + \dfrac{1}{x} = 5$

squaring both side

$\sf \bigg(x + \dfrac{1}{x} \bigg)^{2} = 5$

$\to \sf \bigg(x {}^{2} + \dfrac{1}{x {}^{2} } + 1 \bigg) = 5 {}^{2}$

$\to \sf \bigg(x {}^{2} + \dfrac{1}{x {}^{2} } + 1 \bigg) = 25$

$\to \sf \bigg(x {}^{2} + \dfrac{1}{x {}^{2} } \bigg) = 25 - 1$

$\to \sf \bigg(x {}^{2} + \dfrac{1}{x {}^{2} } \bigg) = 24$

Squaring both side:

$\to \sf \bigg(x {}^{2} + \dfrac{1}{x {}^{2} } \bigg) ^{2} = 24 {}^{2}$

$\to \sf \bigg(x {}^{4} + \dfrac{1}{x {}^{4} } + 1 \bigg) = 576$

$\to \sf \bigg(x {}^{4} + \dfrac{1}{x {}^{4} } \bigg) = 576 - 1$

$\to \sf \bigg(x {}^{4} + \dfrac{1}{x {}^{4} } \bigg) = 575$

$\red{ \rm{}so \: done}$