Question

1)7-5х+х²=0
2)169-х²=0
3)-0,1х²+10=0
4)7х+13-6х²=0
5)3х²-5х-4=0
6)х²-24х=0
7)16х²-4=0
8)5х²=0
9)-х²-3х+15=0
10)х²-5х

Answer 1

1) $7-5x+x^2=0\\x^2-5x+7=0\\d=(-5)^2-4*1*7=25-28=-3$

дискриминант отрицательный, нет решения.

2) $169-x^2=0\\-x^2=-169\\x^2=169\\x1 =13\\x2= -13$

3) $-0,1x^2+10=0\\-x^2+100=0\\-x^2=-100\\x^2=100\\x1=10\\x2=-10$

4)$7x+13-6x^2=0\\-6x^2+7x+13=0\\d=7^2-4*(-6)*13=49312=361=19^2\\x1=\frac{-7+19}{2*(-6)}=\frac{12}{2*(-6)}=-\frac{6}{6} = -1\\x2=\frac{-7-19}{2*(-6)}=\frac{13}{6}$

5) $3x^2-5x-4=0\\d=(-5)^2-4*3*(-4)=25+48=73=\sqrt{73} \\x1=\frac{5+\sqrt{73} }{6} \\x2=\frac{5-\sqrt{73} }{6}$

6) $x^2-24x=0\\x(x-24)=0\\x1=0\\x2=24$

7) $16x^2-4=0\\4x^2-1=0\\4x^2=1\\x^2=\frac{1}{4} \\x1=\frac{1}{2} \\x2= - \frac{1}{2}$

8) $5x^2=0\\x^2=0\\x1=0\\x2=0$

9) $-x^2-3x+15=0\\x^2+3x-15=0\\d=3^2-4*1*(-15)=9+60=69=\sqrt{69} \\x1=\frac{-3+\sqrt{69}}{2} \\x2=\frac{-3-\sqrt{69}}{2}$

10) $x^2-5x=0\\x(x-5)=0\\x1=0\\x2=5$