यदि ` x = (a +sqrt(a^(2)+b^(3)))^(1/3)+(a-sqrt(a^(2)+b^(3)))^(1/3)`, तब ` x^(3) + 3abx - 2a` का मान होगा

Options

A. `2a^(3)`
B. `-2a^(3)`
C. 1
D. 0

Answer

D

Explanation

दिया है ,
` x = (a+sqrt(a^(2)+b^(3)))^(1/3)+ (a-sqrt(a^(2)+b^(3)))^(1/3)`
दोनों पक्षों का घन करने पर ,
` x^(3) = (a+sqrt(a^(2)+b^(3)))+(a-sqrt(a^(2)+b^(3)))`
`+3(a+sqrt(a^(2) +b^(3)))^(1/3) (a-sqrt(a^(3)+b^(3)))^(1/3)`
` {(a + sqrt(a^(2)+b^(3)))^(1/3)+(a-sqrt(a^(2)+b^(3)))^(1/3)}`
` rArr x^(3) = 2a - 3b(x)`
` rArr x^(3) + 3bx - 2a = 0`