Question

If
X+1/x=4


Then,

X^4+1/x^4=?

Answer 1

x+1/x=4
or,x+1=4x
or,3x=1
or,x=1/3

and the answer is...
x^4+1/x^4=(1/3^4+1)/1/3^4=82

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Answer 2

Hey mate !


• Given :

x + 1/x = 4

• To find ;

x⁴ + 1 / x⁴

• Solution :

$\mathsf{x + \frac{1}{x} = 4} \\ \\ \mathsf{on \: squaring \: both \: sides..} \\ \\ \mathsf{(x + \frac{1}{x}) {}^{2} = (4) {}^{2} } \\ \\ \mathsf{x {}^{2} + \frac{1}{x {}^{2} } + 2 = 16 } \\ \\ \mathsf{x {}^{2} + \frac{1}{x {}^{2} } = 16 - 2 } \\ \\ \mathsf{x {}^{2} + \frac{1}{x {}^{2} } =14} \\ \\ \mathsf{on \: squaring \: both \: sides..} \\ \\\mathsf{ (x {}^{2} + \frac{1}{x {}^{2} } ) {}^{2} = (14) {}^{2}} \\ \\\mathsf{x {}^{4} + \frac{1}{x {}^{4} } + 2} = 196 \\ \\ \mathsf{x {}^{4} + \frac{1}{x {}^{4} } = 196 - 2} \\ \\ \boxed{ \bold{x {}^{4} + \frac{1}{x {}^{4} } = 194}}$


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Thanks for the question !