Question

Rezolvati in R ecuatia:
a)(x-3)(x+4)-2(3x-2)=(x-4)la puterea a 2
b)(x+5)(x+2)-3(4x-3)=(x-5)la puterea a2
c)x(x+2)-13=(x-3)(x+3)
d)4x(x-1)=(2x+5)(2x-5)+1

Answer 1

a)(x-3)(x+4)-2(3x-2)=(x-4)²
(x²+4x-3x-12)-(6x-4)=(x²-8x+16)
x²+4x-3x-12-6x+4=x²-8x+16
x²+4x-3x-6x-x²+8x=16+12-4
3x=24
x=24:3
x=8
b)(x+5)(x+2)-3(4x-3)=(x-5)²
(x²+2x+5x+10)-(12x-9)=(x²-10x+25)
x²+2x+5x+10-12x+9=x²-10x+25
x²+2x+5x-12x-x²+10x=25-10-9
5x=6
x=6/5
c)x(x+2)-13=(x-3)(x+3)
x²+2x-13=x²-3²
x²+2x-13=x²-9
x²+2x-x²=-9+13
2x=4
x=4:2
x=2
d)4x(x-1)=(2x+5)(2x-5)+1
5x²-4x=(2x)²-5²+1
5x²-4x=4x²-25+1
5x²-4x-4x²+25-1=0
x²-4x+24=0
a=1
b=-4
c=24
∆=b²-4ac
∆=(-4)²-4×1×24
∆=16-96
∆=-80
∆<0 =>ecuația nu are soluții reale