SOLUTION: pls help me to answer this problem: if x^2-5x+1=0, what is the value of x^4 + 1/x^4

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Question 937913: pls help me to answer this problem: if x^2-5x+1=0, what is the value of x^4 + 1/x^4
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
if x%5E2-5x%2B1=0, what is the value of %28+x%5E4+%2B+1%29%2Fx%5E4+


x%5E2-5x%2B1=0...solve for x then substitute
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-%28-5%29+%2B-+sqrt%28+%28-5%29%5E2-4%2A1%2A1+%29%29%2F%282%2A1%29+
x+=+%285+%2B-+sqrt%28+25-4+%29%29%2F2+
x+=+%285+%2B-+sqrt%28+21+%29%29%2F2+
x+=+%285+%2B-+4.58%29%2F2+


solutions:
x+=+%285+%2B+4.58%29%2F2+
x+=+9.58%2F2+
x+=+4.79
or
x+=+%285+-+4.58%29%2F2+
x+=+0.42%2F2+
x+=+0.21

then substitute:

%28+x%5E4+%2B+1%29%2Fx%5E4+ if x+=+4.79
%28+%284.79%29%5E4+%2B+1%29%2F%284.79%29%5E4+
%28+526.43+%2B+1%29%2F526.43+

+527.43+%2F526.43+

1.002

or
%28+x%5E4+%2B+1%29%2Fx%5E4+ if x+=+0.21
%28+%280.21%29%5E4+%2B+1%29%2F%280.21%29%5E4+
%28+0.00194481+%2B+1%29%2F0.00194481+
+1.002+%2F0.002+

501