SOLUTION: solve x^4+64=20x^2

Question 1205913: solve x^4+64=20x^2
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
subtract 20x^2 from both sides to get:
x^4 + 64 - 20x^2 = 0
arrange in descending order of degree to get:
x^4 - 20x^2 + 64 = 0
let y = x^2 to get:
y^2 - 20y + 64 = 0
factor to get:
(y-4) * (y-16) = 0
solve for y to get:
y = 4 or y = 16
since y = x^2, you get:
x = plus or minus 2 or x = plus or minus 4

your solutions are x = 2, -2, 4, -4

plug each of those into the original equation and the original equation will be true.

for example, when x = 4, x^4 + 64 = 80x^2 becomes 320 = 320, which is true and when x = 2, x^4 + 64 = 20x^2 becomes 80 = 80

here's what it looks like when you graph y = x^4 - 20x^2 + 64.

here's what it looks like when you graph y = x^2 + 64 and you graph y = 20x^2.

the first graph shows the intersection of the graphed equation with y = 0.

the second graph shows the intersection of the two graphed equations.

the x-value of the intersection is the same in both graphs.

RELATED QUESTIONS
Factor {{{8x^3+343}}} Factor... (answered by solver91311)

Factor the expression: x^4-20x^2+64 also,... (answered by edjones)

Please help me solve this equation:... (answered by josmiceli)

Find the other factors of P(x)=x^5-x^4-20x^3+20x^2+64x-64 if you are given that x-4 and... (answered by josgarithmetic,solver91311,ikleyn)

What are the real or imaginary solutions of the polynomial equation? x^4-20x^2+64=0 (answered by LinnW)

I needed to solve this problem and get the solution set: x^4 - 20x^2 + 64 = 0 What... (answered by phillv)

Can someone help me simplify and reduce: 5x^2+20x-160/64-8x I came up with : -5(x-4)/8 (answered by stanbon)

y=-x^2+20x-4 (answered by sofiyac,Alan3354)

Please Solve: 16^x * 4^(x-2) =... (answered by josmiceli)