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Consider biquadratic equation 81x^(4) + ...

Consider biquadratic equation `81x^(4) + 216x^(3)+ 216x^(2) + 96x = 65`, whose roots are `a,b,c,d`. Given `a,b`, real roots and `c,d` are imaginary roots.
On the basis of above information, answer the followin questions:
The Value of `c^(3) + d^(3) - (a+b))^(3)` is equal to

A

`(52)/(9)`

B

`(53)/(9)`

C

`(59)/(9)`

D

`(50)/(9)`

Text Solution

Verified by Experts

The correct Answer is:
A
The given equation is ltbgt `(3x+2)^(4) = 81`
`implies ((3x+2)^(2)-9)((3x+2)^(2)+9)=0`
Let `a=(1)/(3),b=(-5)/(3),C=(-2)/(3)+i,d=(-2)/(3)-i`
Now,verfiy it
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