First slide

Theory of equations

Question

$If x = 2 + 2^{2 / 3} + 2^{1 / 3}, then x^{3} - 6 x^{2} + 6 x =$

Moderate

A

$3$
B

$2$
C

$1$
D

None of these

Solution

$x = 2 + 2^{2 / 3} + 2^{1 / 3} \Rightarrow x - 2 = 2^{2 / 3} + 2^{1 / 3} Cubing both sides, x^{3} - 8 - 6 x^{2} + 12 x = 6 + 6 (x - 2) \Rightarrow x^{3} - 6 x^{2} + 6 x = 2$

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