if x^2-5x=1. find the value of x^2 + 1/x^2
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Step-by-step explanation:
23.
We need to find x^2+1/x^2 = (x+1/x)^2–2
On the other hand, if the roots of equation x^2–5x+1 = 0 are
x1 and x2,
1/x1 = x2 because their product is 1 (according to Vieta’s theorem). So, we need to find
(x1+x2)^2–2 = 5^2–2=23.
The sum x1+x2=5 (also according Vieta’s theorem).
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