Question

Решить уравнение 1)х^2-7х=0 2)4х^2-169=0 3)6х^2+х-2=0 4)3х^2+6х=8х^2-15х

Answer 1

1)х²-7х=0
x(x-7)=0
x=0   x-7=0
         x=7
2)4х²-169=0
4x²=169
x²=$\frac{169}{4}$>0
$x_{1} = \sqrt{ \frac{169}{4} } = \frac{13}{2} =6 \frac{1}{2} =6,5$
$x_{2} =- \sqrt{ \frac{169}{4} } = -\frac{13}{2} =-6 \frac{1}{2} =-6,5$
3)6х²+х-2=0
D=1²-4*6*(-2)=49=7²>0
$x_{1} = \frac{1+ \sqrt{7 ^{2} } }{2*6} = \frac{8}{12} = \frac{2}{3}$
$x_{2} = \frac{1- \sqrt{7 ^{2} } }{2*6} = \frac{-6}{12} = -\frac{1}{2} =-0,5$

4)3х²+6х=8х²-15х
-5x²+21x=0
x(-5x+21)=0
x=0  -5x+21=0
        -5x=-21
         x=4,2