`-27` का घनमूल ज्ञात कीजिए ।

Options

A. `-3,-3omega,-3omega^(2)`
B. `-2,-3omega,-3omega^(2)`
C. `-3,-5omega,-3omega^(2)`
D. `-3,-3omega,-7omega^(2)`

Answer

A

Explanation

माना `x=(-27)^(1//3)`
`rArr" "x^(3)=-27`
`rArr" "x^(3)+27=0rArr(x)^(3)+(3)^(3)=0`
`rArr" "(x+3)(x^(2)-3x+9)=0`
`rArr" "x+3=0` या `x^(2)-3x+9=0`
`x+3=0rArrx=-3` तथा `x^(2)-3x+9=0`
`rArr" "x=(3pmsqrt(9-36))/(2)=(3pmsqrt(-27))/(2)=(3+3sqrt(-3))/(2)`
`=-3((1-+sqrt(-3))/(2)),-3((-1-sqrt(-3))/(2))=-3omega,-3omega^(2)`
अतः `-27` के घनमूल निम्न है - `-3,-3omega,-3omega^(2)`