# Solve for y y^4-17y^2+16=0 y4-17y2+16=0
Substitute u=y2 into the equation. This will make the quadratic formula easy to use.
u2-17u+16=0
u=y2
Factor u2-17u+16 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 16 and whose sum is -17.
-16,-1
Write the factored form using these integers.
(u-16)(u-1)=0
(u-16)(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-16=0
u-1=0
Set the first factor equal to 0 and solve.
Set the first factor equal to 0.
u-16=0
Add 16 to both sides of the equation.
u=16
u=16
Set the next factor equal to 0 and solve.
Set the next factor equal to 0.
u-1=0
Add 1 to both sides of the equation.
u=1
u=1
The final solution is all the values that make (u-16)(u-1)=0 true.
u=16,1
Substitute the real value of u=y2 back into the solved equation.
y2=16
(y2)1=1
Solve the first equation for y.
y2=16
Solve the equation for y.
Take the square root of both sides of the equation to eliminate the exponent on the left side.
y=±16
The complete solution is the result of both the positive and negative portions of the solution.
Simplify the right side of the equation.
Rewrite 16 as 42.
y=±42
Pull terms out from under the radical, assuming positive real numbers.
y=±4
y=±4
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=4
Next, use the negative value of the ± to find the second solution.
y=-4
The complete solution is the result of both the positive and negative portions of the solution.
y=4,-4
y=4,-4
y=4,-4
y=4,-4
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.
Any root of 1 is 1.
y=±1
Any root of 1 is 1.
y=±1
y=±1
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=1
Next, use the negative value of the ± to find the second solution.
y=-1
The complete solution is the result of both the positive and negative portions of the solution.
y=1,-1
y=1,-1
y=1,-1
y=1,-1
The solution to y4-17y2+16=0 is y=4,-4,1,-1.
y=4,-4,1,-1
Solve for y y^4-17y^2+16=0

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