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Question

Calculate 1x31+1x32,, where x1 and x2 are roots of the equation 2x23ax2=0

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Solution

2x23ax2=0
Sum=x1+x2=3a2
Product=x1×x2=1
1x31+1x32=x31+x32(x1x2)3
=(x1+x2)33x1x2(x1+x2)(x1x2)3
=(3a2)33(1)(3a2)12
=27a38+9a21

=(27a3+36a)8


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