Question

if x+1/x=root 2 find the value of x^3+1/x^3

Answer 1

it is interesting to note whether you find x²+1/x² or x³+1/x³ or x⁴+1/x⁴ in case x+1/x=2 answer comes 2
but u have x+1/x=√2
squaring both sides
x²+2+1/x²=2
x²+1/x²=o
so x³+1/x³=(x+1/x)(x²-x×1/x+1/x²)
√2(0-1)
-√2