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Question

If α, β, γ are the roots of cubic equation a x3 + cx = 0. Find the value of  α3β3 +  γ3.


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Solution

Solution: For ax3 + cx = 0

  = x(ax2 + c) = 0

x = 0 or ax2 + c = 0

From the above equation we conclude that one root of equation ax3 + cx should be zero

and Sum of the root = α + β + γ = 0

We know α3β3 +  γ3 = 3αβγ

Since one root is zero

3αβγ = 0

So,α3β3 +  γ3 = 0

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