Question

Solve each of the following equations by using the method of completing the
square:
1. x2 - 6x +3 = 0 2. x2 - 4x + 1 = 0 3. x² + 8x-2=0​

Answer 1

Answer:

Step-by-step explanation:

(1). x² - 6x + 3 = 0

x² - 2*3*x + 3² - 3² + 3 = 0

(x² - 6x + 9) - 6 = 0

(x - 3)² - (√6)² = 0

(x - 3 - √6)(x - 3 + √6) = 0

$x_{1}$ = 3 + √6

$x_{2}$ = 3 - √6

(2). x² - 4x + 1 = 0

x² - 2*2*x + 4 - 4 - 1 = 0

(x - 2)² - (√5)² = 0

(x -2 - √5)(x - 2 + √5) = 0

$x_{1}$ = 2 + √5

$x_{2}$ = 2 - √5

(3). x² + 8x - 2 = 0

(x² + 2*4*x + 16) - 16 - 2 = 0

(x + 4)² - (√18)² = 0

(x + 4 + 3√2)(x + 4 - 3√2) = 0

$x_{1}$ = - 4 - 3√2

$x_{2}$ = - 4 + 3√2