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=−b±D2a=5±292 x1,2=2.5±2.6925824035673 x1=5.1925824035673 x2=−0.19258240356725   Factored form of the equation:  (x−5.1925824035673)(x+0.19258240356725)=0  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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