Question

slove x2-5x+5=0 by completing the square ​

Answer 1

Solution:

x²-5x+5 = 0

=> x² -5x = -5

=> x²- 2*x*(5/2) = -5

=>x² -2*x*(5/2)+(5/2)²

= -5+(5/2)²

=> (x-5/2)² = -5 + 25/4

=> (x-5/2)² = (-20+25)/4

=> (x-5/2)² = 5/4

=> x-5/2 = ±√(5/4)

=> x = 5/2 ±√5/2

=> x = (5±√5)/2

Therefore,

x = (5+√5)/2 or (5-√5)/2

••••

Answer 2

D = b^2 - 4ac = 5^2 - 4×1×5 = 25 - 20 = 5

1st root,

x = (-b + √D)/2a = (-5 + √5)/(2×1) = (-5 + √5)/2

2nd root,

x = (-b - √D)/2a = (-5 - √5)/(2×1) = (-5 - √5)/2

x^2 -5x +5 = {2x/(-5 +√5) }{ 2x/(-5-√5)}

HOPE YOU UNDERSTAND