Question

Wszystkie liczby spełniające równanie 2(x-2)^2=(x-2)(x+3) to:

A. x=-2 i x=-1

B. x=7

C. x=2 i x=7

D. x=1 i x=2

Answer 1

2(x-2)^2=(x-2)(x+3)

2(x²-4x+4)=x²+3x-2x-6

2x²-8x+8=x²+x-6

2x²-8x+8-x²-x+6=0

x²-9x+14=0

Δ=b²-4ac

Δ=(-9)²-4*1*14

Δ=81-56

Δ=25

√Δ=5

 

x1=(9+5)/2=14/2=7

x2=(9-5)/2=4/2=2

Odpowiedź: C

Proszę o naj... :)

Answer 2

2(x-2)^2=(x-2)(x+3)

2( x^2 - 4x + 4) = (x^2 + x -6)

2x^2 - 8x + 8 = x^2 + x - 6

2x^2 - 8x + 8 - x^2 - x +6= 0

x^2 - 9x +14 = 0

Δ= b^2 - 4ac = (-9)^2 - 4*1*14= 81- 56= 25

√Δ= √25 = 5

 

x₁=- b - √Δ/2a= 9 - 5/2*1= 4/2= 2

x₂=-b+√Δ/2a= 9+5/2*1= 14/2 = 7

 

odp. c