Question

if x=3-2root2,find xcube-1/xcube

Answer 1

Answer:

we have , x=3-2√2

1/x=1/3-2√2=1/3-2√2×3+2√2/3+2√2

1/x=3+2√2/(3)²-(2√2)²

1/x=3+2√2/9-(4×2)

1/x=3+2√2/9-8

1/x=3+2√2

x-1/x=(3-2√2)-(3+2√2)

x-1/x=3-2√2-3+2√2

x-1/x=3-3-2√2+2√2

x-1/x=0-0

x-1/x=0

hence, x³-1/x³=(x-1/x)³

we know that, x-1/x=0

so, (x-1/x)³=(0)³

(x-1/x)³=0