Question

Решите уравнения: (x-2)^2+(x-3)^2=2x^2

5+2x=11-7(x-2)

8+3(2x-6)=9

(-5x-3)(2x-1)=0

(x-6)(4x-6)=0

Answer 1

1)

$displaystyle tt (x-2)^2+(x-3)^2=2x^2\displaystyle tt x^2-4x+4+x^2-6x+9=2x^2\displaystyle tt 2x^2-10x+13=2x^2\displaystyle tt -10x+13=0\displaystyle tt -10x=-13\displaystyle tt x=-13div(-10)\displaystyle tt bold{x=1,3}$

2)

$displaystyle tt 5+2x=11-7(x-2)\displaystyle tt 5+2x=11-7x+14\displaystyle tt 5+2x=25-7x\displaystyle tt 2x+7x=25-5\displaystyle tt 9x=20\displaystyle tt x=20div9\\ displaystyle tt bold{x=2frac{2}{9}}$

3)

$displaystyle tt 8+3(2x-6)=9\displaystyle tt 8+6x-18=9\displaystyle tt 6x-10=9\displaystyle tt 6x=9+10\displaystyle tt 6x=19\displaystyle tt x=19cdot6\\ displaystyle tt bold{x=3frac{1}{6}}$

4)

$displaystyle tt (-5x-3)(2x-1)=0\\ displaystyle tt -5x-3=0\displaystyle tt -5x=3\displaystyle tt x=3div(-5)\displaystyle tt bold{x_1=-0,6}\\displaystyle tt 2x-1=0\displaystyle tt 2x=1\displaystyle tt x=1div2\displaystyle tt bold{x_2=0,5}$

5)

$displaystyle tt (x-6)(4x-6)=0\\ displaystyle tt x-6=0\displaystyle tt bold{x_1=6}\\ displaystyle tt 4x-6=0\displaystyle tt 4x=6\displaystyle tt x=6div4\displaystyle tt bold{x_2=1,5}$