Question

Rozw. równanie

a) (3x+4)/(x+2)=(x+8)/(x+5)

b) (3x²+7x+4)=5

Answer 1

A)    (3x+4)/(x+2)=(x+8)/(x+5)
(3x+4)*(x+5) = (x+2)*(x+8)
3x²+15x+4x+20 = x²+8x+2x+16
3x²-x²+15x+4x-8x-2x+20-16 = 0
2x²+9x+4 = 0
delta = b²-4ac
delta = 9²-4*2*4 = 81-32 = 49
pierw. z delty = 7
x1 = -9-7 / 4 = -16/4 = -4
x2 = -9+7 / 4 = -2/4 = -1/2

b)   (3x²+7x+4)=5
3x²+7x+4-5 = 0
3x²+7x-1 = 0
delta = 7²-4*3*(-1) = 49+12 = 61
pierw z delty = pierw z 61 
x1 = -7-pier61 / 6
x2 = -7+pierw61 / 6

Answer 2

A) (3x+4)(x+5)=(x+8)(x+2)
3x^2+19x+20=x^2+10x+16
2x^2+9x+4=0
delta=b^2-4ac
delta=81-4*2*4
delta=49
pierwiastek z delty=7
x1=-9-7/4=-4
x2=-9+7/4=-1/2
b)
3x^2+7x-1=0
delta=61
pierwiastek z delty =pierwiastek z 61
x1=-7-pierwiastek z 61/6
x2=-7+pierwiastek z 61/6