Question

If x+1/x=√5 find x²+1/x² and x⁴+1/x⁴

Answer 1

x+1/x=√5

Then
(x+1/x)²=(√5)²
x²+1/x²+2×x×1/x=5. (a+b)²=a²+b²+2ab
x²+1/x²=5-2
x²+1/x²=3

Now
(x²+1/x²)²=(3)²
x⁴+1/x⁴+2×x×1/x=9
x⁴+1/x⁴=9-2
x⁴+1/x⁴=7

Answer 2

Answer:

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