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Question

Assume that x1 and x2 are roots of the equation 3x2ax+2a1=0. Calculate x31+x32

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Solution

3x2ax+2a1=0
Sum =x1+x2=a3
Product=x1x2=2a13
x31+x32=(x1+x2)33x1x2(x1+x2)
(a3)33(2a13)(a3)
a3272a2a3
=a318a2+9a27
=a27(a218a+9)

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