Question

Sa se calculeze in R: a) 4(x+3)²=(x-5)²
b) (x+2)²=-2x-1
c) (3x+1)²=15x+1
d) (2x-5)²-53=x·(3x-17)
Va rog frumos e URGENT

Answer 1

a) 4(x+3)²=(x-5)²
4(x²+6x+9)=x²-10x+25
4x²+24x+36=x²-10x+25
3x²+34x+11=0
3x²+33x+x+11=0
3x(x+11)+(x+11)=0
(x+11)(3x+1)=0
x+11=0  x=-11
3x+1=0  x=-1/3

b) (x+2)²=-2x-1
x²+4x+4=-2x-1
x²+6x+5=0
x²+5x+x+5=0
x(x+5)+(x+5)=0
(x+5)(x+1)=0
x+5=0  x=-5
x+1=0  x=-1

c) (3x+1)²=15x+1
9x²+6x+1=15x+1
9x²-9x=0
9x(x-1)=0
x=0
x-1=0    x=1

d) (2x-5)²-53=x·(3x-17)4x²-20x+25-53=3x²-17x
x²-3x-28=0
x²+4x-7x-28=0
x(x+4)-7(x+4)=0
(x+4)(x-7)=0
x+4=0    x=-4
x-7=0    x=7