Solve each of the following equations by using the method of completing the square:

Question

Solve each of the following equations by using the method of completing the square: x 2 - 4x + 1 = 0

Philoid · Accepted Answer

Given: x² - 4x + 1 = 0

x² - 4x = - 1

x² - 2.x.2 + 2² = - 1 + 2² (adding 2² on both sides)

(x - 2)² = - 1 + 4 = 3 using a² - 2ab + b² = (a - b)²

(taking square root on both sides)

Hence the roots of equation are