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Question

If x2+x+1=0 then what is the value of (x3+1x3)3 ?

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Solution

Consider x2+x+1=0 and multiply both sides by (x1)
multiply with (x-1) on both sides as shown below:

(x1)(x2+x+1)=0×(x1)(x1)(x2+(x×1)+12)=0x313=0(a3b3=(ab)(a2+ab+b2)x31=0x3=1

Now let us find (x3+1x3)3 as follows:

(x3+1x3)3=(1+11)3=(1+1)3=23=8

Hence, (x3+1x3)3=8

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