polynomials

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for what values of x

x^4+x^2+64 is a perfect square?

including 0, All of these choices -1 8 1 -8

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1 solution

Siddharth Singh
May 8, 2015

All the answers are correct. NOW HOW TO SOLVE THE QUESTION? we can see that all the terms in the given qustion is a perfect square . now if x^4=X^2 then they will be canceled and only 64 would be left which is a perfect sqaure. hence if X^4=x^2 then x^4-x^2=0 x^2(x^2+1) x^2(x-1)(x+1)=0 then from here x =0,-1,+1 now if x^2 = 64 then onlyX^4 will be left which is also a perfect square . so second condition could be x^2=64 from here x=+8,-8. so all the above values are posiible x=0,+1,-1,+8,-8

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