Question

_{x^2+1/x^2=47 then x^2-1/x^2=?}

Answer 1

x²+1/x²=47
By completing the square,
x²+1/x²+2*1/x*x=x²+1/x²+2=47+2
(x+1/x)²=49
x+1/x=√49=7
x²-1/x²=(x+1/x)(x-1/x) -----(1)
(x-1/x)²=x²+1/x²-2=47-2=45
x-1/x=√45=3√5
From (1)
x²-1/x²=7*3√5=21√5