Question

Решите уравнение:
(x+1)^2=(2x+5)^2

Answer 1

х²+2х+1=4х²+20х+25;
х²+2х+1-4х²-20х-25=0;
-3х²-18х-24=0; ÷(-3);
х²+6х+8=0;
D=b²-4ac=36-32=4;
х1,2=-b +- √D /2a= -6 + - 2 / 2;
х1= - 4; х2= - 2.
Ответ. -4. -2

Answer 2

$(x+1)^2=(2x+5)^2 \\ x^{2} +1+2x=4 x^{2} +25+20x \\ x^{2} -4 x^{2} +2x-20x+1-25=0 \\ -3 x^{2} -18x-24=0 \\ 3 x^{2} +18x+24=0/:3 \\ x^{2} +6x+8=0 \\ D=36-32=4 \\ \sqrt{D} =2 \\ x_{1} = \frac{-6+2}{2} =- \frac{4}{2} =-2 \\ \\ x_{2} = \frac{-6-2}{2} =- \frac{8}{2} =-4$