Question

If x-1/x= under root 3, find x^2+1/x^2

Answer 1

x- 1/x =√3

(x-1/x)^2 =x^2+1/x^2 - 2(x)(1/x)
=>x^2+1/x^2= (x-1/x)^2+2=(√3)^2+2=3+2=5
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Answer 2

x-1==√3x
x-√3x-1=0

x=1/(1-√3)

x^2+(1/x^2)=?
or; (1-√3)^2 +1/(1-√3)^2=?

=(1+3-2√3+1)/(1+3-2√3)
=(5-2√3)/(4-2√3)
{using a^2 -b^2= (a+b)(a-b) ],
Rationalising the denominator;
=[(5-2√3)/(4-2√3)]×[(4+2√3)/(4+2√3)]
=(20-8√3+10√3-12)/(16-12)
=(8+2√3)/4
=2+(√3/2)

Hope this helps!