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Let x=(sqrt(50)+7)^(1//3)-(sqrt(50)-7)^(...

`Let x=(sqrt(50)+7)^(1//3)-(sqrt(50)-7)^(1//3)`.Then-

A

x=2

B

x=3

C

x is a rational number, but not an integer

D

x is an irrational number

Text Solution

Verified by Experts

The correct Answer is:
A
`x=(sqrt(50)+7)^(1//3)-(sqrt(50)+7)^(1//3)`
`x^(3)=(sqrt(50)+7)-(sqrt(50)-7)-3(sqrt(50)+7)(sqrt(50)+7)^(1//3)-(sqrt(50)-7)-(sqrt(50)+7)^(1//3)`
`x^(3)=14-3(1)(x)`
`x^(3)=14-3x`
`x^(3)+3-14=0`
x=2
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