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Chapter 9: Q. 167 (page 906)

In the following exercises, solve. (x2+1)2-5(x2+1)+4=0

Short Answer

Expert verified

Solution for equation will be

  • x=+3
  • x=-3
  • x=+0
  • x=-0

Step by step solution

01

Step 1.  Given Data 

Quadratic Equation is(x2+1)2-5(x2+1)+4=0

02

Step 2.  To Find  

We have to solve it and find the value of x.

03

Step 3.  Explanation  

Let the value of(x2+1)=u

Then the equation is -

(x2+1)2-5(x2+1)+4=0

Put the value of (x2+1)=u

u2-5u+4=0

(u-4)(u-1)=0

By using Zero product property -

u-4=0, u-1=0

u=4, u=1

04

Step 4.  Calculation  

Replace u with (x2+1)

x2+1=4, x2+1=1

x2=4-1, x2=1-1

x2=3, x2=0

x=卤3, x=卤0

There are four solutions -

  • x=+3
  • x=-3
  • x=+0
  • x=-0

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