Let xx be a real number. What is the minimum value of x2−4x+3x2−4x+3?
Answer:
−1−1
- We are given a quadratic equation x2−4x+3x2−4x+3, where x is a real number and we need to find the minimum value of this equation.
- Now, we have,
x2−4x+3=x2−4x+4−1=x2−2(2)x+22−1=(x−2)2−1 - Observe that the value of x2−4x+3 will be minimum when (x−2)2=0,i.e. x=2
The value of x2−4x+3 at x=2 is −1. - Hence, the minimum value of x2−4x+3 is −1.