SOLUTION: (4x^4/3)+(7x^2/3)=2 solve the equation (hint-quadratic in form)

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Question 863593: (4x^4/3)+(7x^2/3)=2 solve the equation (hint-quadratic in form)
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Choose some variable, and for example, u;
u=x%5E%282%2F3%29.

4u%5E2%2B7u=2
4u%5E2%2B7u-2=0
discriminant is 7*7-4*4*(-2)=49+32=81.
u=%28-7-sqrt%2881%29%29%2F%282%2A4%29=-16%2F8=-2
OR
u=%28-7%2B9%29%2F8=2%2F8=1%2F4
-
Reverse the substitution and find x.
x%5E%282%2F3%29=-2
x=%28-2%29%5E%283%2F2%29
x=%28-8%29%5E%281%2F2%29
highlight%28x=2i%2Asqrt%282%29%29------?.
-
x%5E%282%2F3%29=1%2F4
x=%281%2F4%29%5E%283%2F2%29
x=%282%5E-2%29%5E%283%2F2%29
x=2%5E%28-3%29
highlight%28x=1%2F8%29