Question

Алгебра 10-11 класс даю 40 балов
$3x {}^{2} + 2 \sqrt{x {}^{2} + 5x + 1 } = 2 - 15x$

Answer 1

$3x^{2}+2\sqrt{x^{2}+5x+1 }=2-15x\\\\(3x^{2}+15x+3)-5+2\sqrt{x^{2}+5x+1 }=0\\\\3(x^{2}+5x+1)+2\sqrt{x^{2}+5x+1 }-5=0\\\\\sqrt{x^{2}+5x+1 }=m,m\geq 0\\\\3m^{2}+2m-5=0\\\\D=2^{2}-4*3*(-5)=4+60=64=8^{2}\\\\m_{1}=\frac{-2+8}{6}=1\\\\m_{2}=\frac{-2-8}{6}=-\frac{10}{6} <0$

m₂ - не подходит

$\sqrt{x^{2}+5x+1 }=1\\\\(\sqrt{x^{2}+5x+1 })^{2}=1^{2}\\\\x^{2}+5x+1=1\\\\x^{2}+5x=0\\\\x(x+5)=0\\\\x_{1}=0\\\\x_{2}=-5$

Проверка :

$1)3*0^{2}+2\sqrt{0^{2}+5*0+1 } =2-15*0\\\\0+2=2-0\\\\2=2\\\\2)3*(-5)^{2}+2\sqrt{(-5)^{2}+5*(-5)+1 }=2-15*(-5)\\\\75+2*1=2+75\\\\77=77$

Ответ : - 5 ; 0

Answer 2

Решение задания приложено