Question

Спростить вираз:
5b(-0,2b⁶)³
Розв’язати систему рівнянь:
{
(х − 1)
2 − (х + 2)
2 = 3у,
{(у − 3)
2 − (у + 2)
2 = 5х.

Answer 1

Пояснення:

1)

$5b*(-0,2b^6)^3=5b*(-0,2)^3*b^{6*3}=5b*(-0,008)*b^{18}=-0,04b^{18+1}=-0,04b^{19}$

2)

$\displaystyle\\\left \{ {{(x-1)^2-(x+2)^2=3y} \atop {(x-3)^2-(y+2)^2=5x}} \ \ \ \ \ \ \left \{ {{(x-1+x+2)*(x-1-x-2)=3y} \atop {(y-3+y+2)*(y-3-y-2)=5x}} \right.$

$\displaystyle\\\left \{ {{(2x+1)*(-3)=3y} \atop {(2y-1)*(-5)=5x}} \right. \ \ \ \ \ \ \left \{ {{-6x-3=3y} \atop {-10y+5=5x}} \right. \ \ \ \ \ \ \left \{ {{6x+3y=-3\ |:3\atop {5x+10y=5\ |:5}} \right. \\\\\\\left \{ {{2x+y=-1} \atop {x+2y=1}} \right. \ \ \ \ \left \{ {{2*(1-2y)+y=-1} \atop {x=1-2y}}\ \ \ \ \left \{ {{2-4y+y=-1} \atop {x=1-2y}} \right. \right.$

$\displaystyle\\\left \{ {{3y=3\ |:3} \atop {x=1-2y}} \right. \ \ \ \ \ \ \left \{ {{y=1} \atop {x=-1}} \right. .$

Відповідь: (-1;1).