How to solve x^4-20x^2+64=0?
Thanks for your time :]
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This is a quadratic equation in x^2.
Put u = x^2 ………….(1)
u^2 – 20u + 64 = 0
(u – 16)(u – 4) = 0
u = 16 or u = 4.
Hence from (1):
x = +/-sqrt(u) = +/-4 or +/- 2.
[x^2-4][x^2-16]. Now, both of these factors can be further factorised, as they are both the difference of two squares,
x^2-4 = [x+2][x-2], and x^2-16 = [x+4][x-4], so the complete factorisation is:
[x+2][x-2][x+4][x-4 = 0, giving as solutions,
x=-2, x=2, x=-4, and x=4. Hope this helps, Twiggy.
find 2 numbers that multiply to 64 and add to -20 which is -16 and -4
then you find what x should be to make the equation true wich is x^2
the equation is now
(x^2-16)(x^2-4)=0
to finnish, you take one equation at a time so
x^2-16 turns to x^2=16 which simplifies to x= + or – 4
do the same with x^2-4 making it x=+ or – 2
so x=+-4 or +-2
4 – 20, 2 + 64.
The answer is -16 and 66. In other words, -82.
(x-4)(x+4)(x-2)(x+2)=0
x=4 V x= -4 V x=2 V x= -2
It is the best answer.
The previous answers are false
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