Expression with powers

If x-1/x=5, find the value of x4+1/x4

Correct answer:

v =  727

Step-by-step explanation:

x−1/x=5 x2−1=5x  x2−5x−1=0  a=1;b=−5;c=−1 D=b2−4ac=52−4⋅1⋅(−1)=29 D>0  x1,2​=2a−b±D​​=25±29​​ x1,2​=2.5±2.692582 x1​=5.192582404 x2​=−0.192582404  v1​=x14​+1/x14​=5.19264+1/5.19264=727 v2​=x24​+1/x24​=(−0.1926)4+1/(−0.1926)4=727  v1​=v2​ v=v1​=727

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