Find the roots of the following quadratic equations (if they exist)by the mnethod of completion of the square .

Question

(i) x^2-(root2+1)+root2=0

Answer 1

x^2 - (√2+1)x + √2 = 0
x^2 - (√2+1)x + ((√2+1)/2)^2 + √2 = ((√2+1)/2)^2
(x - (√2+1)/2)^2 = 1/4 (√2-1)^2
x - (√2+1)/2 = ±1/2 (√2-1)
x = (√2+1)/2 ± 1/2 (√2-1)
x = √2,1

The method works, but it's a lot of work. Just by inspection it was clear that we had

(x-√2)(x-1)