Question

if x=3 + 2 √2 ,find x 3 - 1 / x3

Answer 1

Answer:

Step-by-step explanation:

x=3+2√2

1/x=1/(3+2√2)

Rationalizing the denominator by multiplying both numerator and denominator by 3-2√2 we get,

1/x=3-2√2

x-1/x=3+2√2-3+2√2

=4√2

(x-1/x)²=x²+1/x²-2

x²+1/x²=(4√2)²+2

=34

x³-1/x³=(x-1/x) (x²+1+1/x²)

=(4√2) (35)

=140√2

Hope it helps