Write x² - 6x + 7 = 0 in the form (x - a)² = b, where a and b are integers.

Solution:

Given that: x² - 6x + 7 = 0

To convert the above equation into a perfect square we add 9 on the left hand side and hence we have to subtract too on the same side.

We have

x² - 6x + 9 - 9 + 7 = 0

(x² - 6x + 9) - 9 + 7

By Splitting the middle term, we get

x² - 3x - 3x + 9 - 2 = 0

x(x - 3) - 3(x - 3) = 2

(x - 3)(x - 3) = 2

(x - 3)² = 2

Write x² - 6x + 7 = 0 in the form (x - a)² = b, where a and b are integers.

Summary:

The given equation x² - 6x + 7 = 0 is written as (x - 3)² = 2.