Question

Rozwiąż równanie 2x+3/x-2=x+1/x+2

Answer 1

załącznik:

Answer 2

2x+3          x+1

------   =   --------

x-2            x+2

                                                Z: x-2 ≠ 0

                                                    x ≠ 2

                                                    x+2 ≠ 0

                                                    x ≠ -2

                                                D = R \ {-2;2}

Z proporcji otrzymujemy:

(2x+3)(x+2) = (x+1)(x-2)

2x²+4x+3x+6 = x²-2x+x-2

2x²+7x+6 = x²-x-2

2x²-x²+7x+x+6+2 = 0

x²+8x+8 = 0

Δ = b²-4ac = 64-32 = 32

√Δ = √32 = √(16·2) = √16·√2 = 4√2 

x1 = (-b-√Δ)/2a = (-8-4√2)/2 = -4-2√2   ∈ D

x2 = (-b+√Δ)/2a = (-8+4√2)/2 = -4+2√2  ∈ D

Odp. x = -4-2√2   v   x = -4+2√2