1.

यदि `x=2-2^(1//3)+2^(2//3)` है तो `x^(3)-6x^(2)+18x+18` का मान ज्ञात करें।A. 22B. 33C. 40D. 45

Answer» Correct Answer - C
`x=2-2^(1//3)+2^(2//3)`
`x-2=2^(2//3)-2^(1//3)`………….i
Take cube both sides
`(x-2)^(3)=(2^(2//3)-2^(1//3))^(3)`
`x^(3)-8-6x(x-2)-(2^(2//3))^(3)-(2^(1//3))^(3)`
`-3xx2^(2//3).2^(1//3)(2^(2//3)-2^(1//3))`
`x^(3)-8-6x^(2)+12x`
`=2^(2)-2-3xx2(2+1)/3(x-2)`
From equation i
`:. x^(3)-8-6x^(2)+12x`
`=4-2-2x2(x-2)`
`x^(3)-8-6x^(2)+12x=2-6x+12`
`x^(3)+18x-6x^(2)-8-14=0`
`x^(3)+18x-6x^(2)-22=0`
`:. x^(3)-6x^(2)+18x+18=22+18=40`


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