If x = √2 + √3, find x³ - 3x.
Show answer & explanation
Correct answer: C
Explanation
Given:
x = √2 + √3
By the formula:
(a + b)³ = a³ + b³ + 3ab(a + b)
x³ = (√2 + √3)³
= (√2)³ + (√3)³ + 3√2√3(√2 + √3)
= 2√2 + 3√3 + 3√6(√2 + √3)
= 2√2 + 3√3 + 3(√12 + √18)
= 2√2 + 3√3 + 3(2√3 + 3√2)
= 2√2 + 3√3 + 6√3 + 9√2
= 11√2 + 9√3
x³ − 3x= (11√2 + 9√3) − 3(√2 + √3)
= 11√2 + 9√3 − 3√2 − 3√3
= 8√2 + 6√3