Expression with powers

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

Correct answer:

v =  727

Step-by-step explanation:

x1/x=5 x21=5x  x25x1=0  a=1;b=5;c=1 D=b24ac=5241(1)=29 D>0  x1,2=2ab±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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