If x = ³√ a + √a² + b³ + ³√a

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If x = ³√ a + √a² + b³ + ³√a - √a² + b³ , then x³ + 3bx is equal to

1. 0
2. a
3. 2 a
4. 1

Correct Option: C

x = ³√ a + √a² + b³ + ³√a - √a² + b³
Cubing both sides,
x³ = (³√ a + √a² + b³)³ + (³√a - √a² + b³)³ + (³√ a + √a² + b³)
(³√a - √a² + b³)(³√ a + √a² + b³ + ³√a - √a² + b³)
= a + √a² + b³ + a - √a² + b³ + 3 (a + √a² + b³ × a - √a² + b³)^¹/₃x
= 2a + 3(a² - a² - b³)^¹/₃x
= 2a + ( - 3bx)
∴ x³ + 3bx = 2a