Question

Solve the following quadratic equation. Give your answer correct to three significant figures. (x−1)2 −3x+4=0

Answer 1

We have to solve the quadratic equation, (x - 1)² - 3x + 4 = 0 where our answer should be correct upto three significant figures.

Solution : equation is , (x - 1)² - 3x + 4 = 0

Here we use (a - b)² = a² - 2ab + b²

so, (x - 1)² = x² - 2x + 1

⇒(x² - 2x + 1) - 3x + 4 = 0

⇒x² - 5x + 5 = 0

⇒x² - 5x = - 5

⇒x² - 2(5/2)x + (5/2)² = -5 + (5/2)²

⇒(x - 5/2)² = -5 + 25/4 = 5/4

Taking square root both sides,

⇒(x - 5/2) = ±√5/2

⇒x = 5/2 ± √5/2

⇒x = (5 ± √5)/2

Let's take √5 ≈ 2.24

so, x = (5 ± 2.24)/2 = 3.62 , 1.38

Therefore the values of x are, 3.62 and 1.38