Question

Solve each equation. Label any extraneous solutions as well.

Answer 1

1

• Square on both the sides
• 2x - 3 = (x - 3)²
• 2x - 3 = x² + 9 - 6x [(a+b)²=a²+b²+2ab]
• x² + 9 - 6x - 2x + 3 = 0
• x² - 8x + 12 = 0
• x² - 6x - 2x +12 = 0
• x(x - 6) - 2(x - 6)
• (x - 6)(x - 2)
• x = 6 or x = 2

2

• Square on both the sides
• 3x - 2 = (x - 2)²
• 3x - 2=x² + 4 - 4x
• x² - 4x - 3x + 4 + 2
• x² - 7x + 6
• x² - 6x - 1x + 6
• x(x - 6) - 1(x - 6)
• (x - 6)(x - 1)
• x = 6 or x = 1

3

• Square on both the sides
• 2x + 6 = (x - 1)²
• 2x + 6 = x² - 2x + 1
• x² - 2x - 2x + 1 - 6 = 0
• x² - 4x - 5= 0
• x² + 1x - 5x - 5 = 0
• x(x + 1) - 5(x + 1)
• (x + 1)(x - 5)
• x = - 1 or x = 5