Question

(x-1) whole square =9
​

Answer 1

Required Answer:-

Given:

• (x - 1)² = 9

To Find:

• The values of x.

Answer:

• x = 4, -2

Solution:

Given that,

→ (x - 1)² = 9

Using identity (a - b)² = a² - 2ab + b², we get,

→ x² - 2x + 1 = 9

→ x² - 2x + 1 - 9 = 0

→ x² - 2x - 8 = 0

→ x² - 4x + 2x - 8 = 0

→ x(x - 4) + 2(x - 4) = 0

→ (x + 2)(x - 4) = 0

Therefore,

→ x + 2 = 0 or x - 4 = 0

→ x = -2, 4

Alternative method:

Given,

→ (x - 1)² = 9

→ (x - 1) = √9

→ x - 1 = ±3

So, when x - 1 = 3,

→ x - 1 = 3

→ x = 1 + 3

→ x = 4

Again, when x - 1 = -3

→ x - 1 = -3

→ x = 1 - 3

→ x = -2

Thus,

→ x = 4, -2.