Question

Решите уравнение:
1)x²+7|x|+10=0;
2)x²-29|x|+30=0;
3)x²-11|x|+30=0;​

Answer 1

$1)\ \ x^2+7|x|+10=0\\\\a)\ \ x\geq 0\ ,\ \ x^2+7x^2+7x+10=0\ \ ,\ \ x_1=-5<0\ ,\ x_2=-2<0\\\\b)\ \ x<0:\ \ x^2-7x+10=0\ \ ,\ \ x_3=2>0\ ,\ x_4=5>0\\\\Otvet:\ \ x\in \varnothing \ .$

$2)\ \ x^2-29|x|+30=0\\\\a)\ \ x\geq 0:\ x^2-29x+30=0\ \ ,\ \ x_{1,2}=\dfrac{29\pm \sqrt{721}}{2}\\\\b)\ \ x<0:\ \ x^2+29x+30=0\ \ ,\ \ x_{3,4}=\dfrac{-29\pm \sqrt{721}}{2} \\\\Otvet:\ \ x_{1,2}=\dfrac{29\pm \sqrt{721}}{2}\ ,\ x_{3,4}=\dfrac{-29\pm \sqrt{721}}{2} \ .$

$3)\ \ x^2-11|x|+30=0\\\\a)\ \ x\geq 0:\ x^2-11x+30=0\ \ ,\ \ x_1=5\ ,\ x_2=6\\\\b)\ \ x<0:\ \ x^2+11x+30=0\ \ ,\ \ x_3=-6\ ,\ x_4=-5\\\\Otvet:\ \ x=5\ ,\ x=6\ ,\ x=-6\ ,\ x=-5\ .$