solve the equation after making an appropriate substitution x^4-22x^2+96=0
This equation factors.
x^{4} - 22x^{2 }+ 96=0
(x^{2 }- 16)(x^{2} - 6) = 0
x^{2} = 16 or 6
x = ±4 or ±√6
solve the equation after making an appropriate substitution x^4-22x^2+96=0
This equation factors.
x^{4} - 22x^{2 }+ 96=0
(x^{2 }- 16)(x^{2} - 6) = 0
x^{2} = 16 or 6
x = ±4 or ±√6
You could make a substitution u = x^{2}
You can rewrite x^{4} - 22x^{2} + 96 = 0 as
(x^{2})^{2} - 22(x^{2}) + 96 = 0 which makes it easier to see where to make the substitution:
u^{2} - 22u + 96 = 0
now factor it by finding two numbers which multiply to equal 96, and add up to -22: (-6)*(-16) = 96 and (-6) + (-16) = -22
(u - 16)(u - 6) = 0
u = 16 or u = 6. Remember that u = x^{2} and now you can solve it as Roman did.