# Solve for y y^4-8y^2-9=0

y4-8y2-9=0
Substitute u=y2 into the equation. This will make the quadratic formula easy to use.
u2-8u-9=0
u=y2
Factor u2-8u-9 using the AC method.
Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is -9 and whose sum is -8.
-9,1
Write the factored form using these integers.
(u-9)(u+1)=0
(u-9)(u+1)=0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
u-9=0
u+1=0
Set the first factor equal to 0 and solve.
Set the first factor equal to 0.
u-9=0
Add 9 to both sides of the equation.
u=9
u=9
Set the next factor equal to 0 and solve.
Set the next factor equal to 0.
u+1=0
Subtract 1 from both sides of the equation.
u=-1
u=-1
The final solution is all the values that make (u-9)(u+1)=0 true.
u=9,-1
Substitute the real value of u=y2 back into the solved equation.
y2=9
(y2)1=-1
Solve the first equation for y.
y2=9
Solve the equation for y.
Take the square root of both sides of the equation to eliminate the exponent on the left side.
y=±9
The complete solution is the result of both the positive and negative portions of the solution.
Simplify the right side of the equation.
Rewrite 9 as 32.
y=±32
Pull terms out from under the radical, assuming positive real numbers.
y=±3
y=±3
The complete solution is the result of both the positive and negative portions of the solution.
First, use the positive value of the ± to find the first solution.
y=3
Next, use the negative value of the ± to find the second solution.
y=-3
The complete solution is the result of both the positive and negative portions of the solution.
y=3,-3
y=3,-3
y=3,-3
y=3,-3
Solve the second equation for y.
(y2)1=-1
Solve the equation for y.
Take the 1th root of each side of the equation to set up the solution for y
(y2)1⋅11=-11
Remove the perfect root factor y2 under the radical to solve for y.
y2=-11
Take the square root of both sides of the equation to eliminate the exponent on the left side.
y=±-11
The complete solution is the result of both the positive and negative portions of the solution.
Simplify the right side of the equation.
Evaluate -11 as -1.
y=±-1
Rewrite -1 as i.
y=±i
y=±i
The complete solution is the result of both the positive and negative portions of the solution.
First, use the positive value of the ± to find the first solution.
y=i
Next, use the negative value of the ± to find the second solution.
y=-i
The complete solution is the result of both the positive and negative portions of the solution.
y=i,-i
y=i,-i
y=i,-i
y=i,-i
The solution to y4-8y2-9=0 is y=3,-3,i,-i.
y=3,-3,i,-i
Solve for y y^4-8y^2-9=0

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