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If x-=2+^(2//3)"then the value"(x^(3)-6x...

If `x-=2+^(2//3)"then the value"(x^(3)-6x^(2)+6x)is`

A

`0`

B

`2`

C

`3`

D

`4`

Text Solution

Verified by Experts

The correct Answer is:
B
`x=2+2^(2/3)+2^(1/3)`
`=x-2=2^(2/3)+2^(1//3)`………..i
घन करने पर
`(x-2)^(3)=(2^(2//3)+2^(1//3))^(3)`
`impliesx^(3)-8-6x^(2)+12x`
`=(2^(2//3))^(3)=(2^(1//3))^(3)+3.2^(2//3).2^(1//3)(2^(2//3)+2^(1//3))`
`impliesx^(3)-6x^(2)+12x-8=4+2=3.(2)^(2/3+1/3)(2^(2//3)+2^(1//3))`
`impliesx^(3)-6x^(2)+12x-8=6+3(2){x-2}` (समी (i) से)
`impliesx^(3)-6x^(2)+12x-8=6+6x-12`
`:.x^(3)-6x^(2)+6x=2`
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