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

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.

u-16=0

Add 16 to both sides of the equation.

u=16

u=16

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

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

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