Rozwiązane

x pierwiastka 2 - 3= x- 1

Odpowiedź :

x pierwiastka 2 - 3= x- 1
x√2 -3 = x -1
x√2 = x -1 +3
x√2 = x +2 /()²
( x√2 )² = ( x +2)²
2x² = x² +4x +4
2x² -x² -4x -4 = 0
x² -4x -4 = 0

a =1
b=-4
c =-4

Δ= b² -4ac
Δ = (-4)² -4*1*(-4)
Δ = 16 + 16
Δ = 32
√Δ = √32
√Δ = 4√2

x₁ = (-b-√Δ):2a
x₁ = [ -(-4) -4√2] :2*1 = (4 -4√2):2 = 2 -2√2
x₁ = 2-2√2

x₂= (-b-√Δ):2a
x₂ = [-(-4) +4√2] :2*1 = (4 +4√2):2 = 2 + 2√2
x₂ = 2 + 2√2

x₁ = 2 - 2√2
x₂ = 2 + 2√2

Viz Inne Pytanie