1.

यदि `x=root(3)(a+sqrt(a^(2)+b^(3)))+root(3)(a-(a^(2)-b^(3))` है तो `x^(3)+3bx` किसके बराबर है?

Answer» Correct Answer - C
`x=root(3)(a+sqrt(a^(2)+b^(3))+root(3)(a-sqrt(a^(2)+b^(3))`
Take cube on the both sides
`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^(2)+b^(3)))^(1/3)`
`(root(3)(a+sqrt(a^(2)+b^(3)))+root(3)(a-sqrt(a^(3)+b^(3))))`
`x^(3)=2a+3(a^(2)-(a^(2)+b^(3)))^(1/3)xx x`
`x^(3)=2a+3(-b^(3))^(1/3)(x)`
`x^(3)=2a+3(-b^(3))^(1/3)(x)`
`x^(3)=2a-3bx`
`x^(3)+3bx=2a`


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