Here, if we let u = x2, we can rewrite the equation so it looks like an ordinary quadratic equation:
u2 − 20u + 64 = 0
We now factor to give:
(u − 16)(u − 4) = 0
So the solutions for u are 16 or 4.
So `x^2= 16` or `x^2= 4`.
These give us:
|x = −4 or 4||x = −2 or 2|
So the complete set of solutions is: `x = −4, −2, 2, 4`.
Is it correct?
The sketch shows:
`y = x^4 - 20x^2 + 64`, showing intersections with the x-axis
We can see from where the graph cuts the x-axis that the solutions are correct.
Get the Daily Math Tweet!
IntMath on Twitter