Question

if x+1/x= √5 , then find x²+1/x² Pls help fast

Answer 1

x+1/x=√5
squaring both sides
(x+1/x)^2=(√5)^2
x^2+2*x*1/x+1/x^2=5
x^2+2+1/x^2=5
x^2+1/x^2=5-2
x^2+1/x^2=3..

Answer 2

squaring both side
${(x + \frac{1}{x} )}^{2} = ({ \sqrt{5}) }^{2} \\ {x}^{2} + ({ \frac{1}{x} )}^{2} + 2 \times x \times \frac{1}{x} = 5 \\ {x}^{2} + \frac{1}{ {x}^{2} } = 5 - 2 \\ {x}^{2} + \frac{1}{ {x}^{2} } = 3$
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