1. ## Completing the square/Quadratics

Find the positive constant a and b such that x^4+9/x^4 = (x^2-a/x^2)^2 + b for all non-zero values of x.

Hence write down or obtain otherwise, the least possible value of x^4+9/x^4 for real values of x.

Please show a step by step approach to the problem. Thanks

2. Originally Posted by umeirhuss
Find the positive constant a and b such that x^4+9/x^4 = (x^2-a/x^2)^2 + b for all non-zero values of x.

Hence write down or obtain otherwise, the least possible value of x^4+9/x^4 for real values of x.

Please show a step by step approach to the problem. Thanks
Have you tried expanding the RHS and see how it can be compared to be the LHS?

3. in other words, what is $\displaystyle (x^2- a/x^2)^2$? How does that differ from $\displaystyle (x^4+ 9/x^4)$?

4. i try to but i got stuck and don't know where to go... i got a=3 but no answer for b!! I guess I'm doing something wrong. your help will be much appreciated. Thanks

5. Originally Posted by HallsofIvy
in other words, what is $\displaystyle (x^2- a/x^2)^2$? How does that differ from $\displaystyle (x^4+ 9/x^4)$?
what about the value of b?