Question

1.rozwiaz rownania

a)2x²+7x-4=0
b) x(4x-23)(23·2x-6)=0
c) (x²-23²)(x²+3x-4)=0
d)4x³-4x²+x=0

Answer 1

A)
2x²+7x-4=0
Δ=7² + 4*2*4= 49+32 = 81
x=(-7-9)/4 = -4  v  x=(-7+9)/4=2/4=1/2
x∈{-4, 1/2}
b)
x=0  v  4x-23=0  v  46x-6=0
x=0  v  x=23/4=5,75  v  x=6/46=3/23
x∈{0, 3/23, 5,75}
c)
x²-23²=0  v  x²+3x-4=0
(x+23)(x-23)=0   v  x²+4x-x-4=0
x=-23  v  x=23  v  x(x+4)-(x+4)=0
(x+4)(x-1)=0
x=-4  v  x=1
Odp. x∈{-23, -4, 1, 23}
d)
4x³-4x²+x=0
x(4x²-4x+1)=0
x(2x-1)²=0
x=0  v  2x-1=0
2x=1
x=1/2
Odp. x∈{0, 1/2}