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Chapter 9: Q. 536 (page 988)

Solve each equation.

4x4-17x2+4=0

Short Answer

Expert verified

The required solution is:

x=-2,x=-12,x=12,x=2

Step by step solution

01

Step 1. Given information.

We have:

4x4-17x2+4=0

02

Step 2. Rewrite the equation as standard form 

Rewrite the equation with u=x2鈥�and鈥�u2=x4.

4u2-17u+4=0

03

Step 3. Solve the quadratic equation.

We have:

4u2-17u+4=0

The quadratic equation of the form ax2+bx+c=0, the solutions are:

x1,鈥�2=-b卤b2-4ac2aFor鈥�a=4,鈥�b=-17,鈥�c=4u1,鈥�2=--17卤-172-4路鈥�4路鈥�42路鈥�4u1=--17+152路鈥�4,鈥�u2=--17-152路鈥�4u=4,鈥�u=14

Substitute back u=x2:

x2=4,鈥�x2=14x=4,x=14x=-2,2,-12,12

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