#1
по 5-x
по 10-y
{x+y=25|*10
{5x+10y=150
-{10x+10y=250
-{5x+10y=150
5x=100|:5
x=20
20+y=25
y=25-20
y=5
#2
математика-x
география-y
{x+y=100
{x=y+30
Формула сокращенного умножения куб суммы.
![(10 x^{3} )^{3} +3(10x^{3} )^{2} \frac{1}{3} y^{2} +3*10x^{3}( \frac{1}{3} y^{2})^{2}+( \frac{1}{3} y^{2})^{3}=(10 x^{3}+ \frac{1}{3} y^{2} )^{3}](https://tex.z-dn.net/?f=+%2810+x%5E%7B3%7D+%29%5E%7B3%7D+%2B3%2810x%5E%7B3%7D+%29%5E%7B2%7D++%5Cfrac%7B1%7D%7B3%7D+y%5E%7B2%7D+%2B3%2A10x%5E%7B3%7D%28+%5Cfrac%7B1%7D%7B3%7D+y%5E%7B2%7D%29%5E%7B2%7D%2B%28+%5Cfrac%7B1%7D%7B3%7D+y%5E%7B2%7D%29%5E%7B3%7D%3D%2810+x%5E%7B3%7D%2B+%5Cfrac%7B1%7D%7B3%7D++y%5E%7B2%7D++%29%5E%7B3%7D)
Sin²4x - cos²4x > -0.5
cos²4x - sin²4x < ½
cos8x < ½
8x ∈ (π/3 + 2πn; 5π/3 + 2πn), n ∈ ℤ
x ∈ (π/24 + πn/4; 5π/24 + πn/4), n ∈ ℤ
Ответ: x ∈ (π/24 + πn/4; 5π/24 + πn/4), n ∈ ℤ
![x^2+y^2+6x-4y+14=(x^2+6x)+(y^2-4y)+14=\\\\=(x+3)^2-9+(y-2)^2-4+14=\underbrace {(x+3)^2}_{\geq 0}+\underbrace {(y-2)^2}_{\geq 0}+1\geq 1](https://tex.z-dn.net/?f=x%5E2%2By%5E2%2B6x-4y%2B14%3D%28x%5E2%2B6x%29%2B%28y%5E2-4y%29%2B14%3D%5C%5C%5C%5C%3D%28x%2B3%29%5E2-9%2B%28y-2%29%5E2-4%2B14%3D%5Cunderbrace+%7B%28x%2B3%29%5E2%7D_%7B%5Cgeq+0%7D%2B%5Cunderbrace+%7B%28y-2%29%5E2%7D_%7B%5Cgeq+0%7D%2B1%5Cgeq+1)
Наименьшее значение выражения - это 1 .