(5x² - 12x + 4)/(6 - 15x) = 5(x - 0,2)(x - 2) / 3(2 - 5x) =
= 5(x - 0,2)(x - 2) / - 15(x - 0,2) = - (x - 2) /3 = (2 - x) /3
Стороны прямоугольника через диагональ :
2*
![d^{2}](https://tex.z-dn.net/?f=+d%5E%7B2%7D+)
= 2*
![a^{2}](https://tex.z-dn.net/?f=+a%5E%7B2%7D+)
+ 2*
![b^{2}](https://tex.z-dn.net/?f=+b%5E%7B2%7D+)
d= корню из (
![a^{2}](https://tex.z-dn.net/?f=+a%5E%7B2%7D+)
+
![b^{2}](https://tex.z-dn.net/?f=+b%5E%7B2%7D+)
)
![a^{2} + b^{2}](https://tex.z-dn.net/?f=+a%5E%7B2%7D+%2B+b%5E%7B2%7D+)
= 61
Система уравнений:
2a+2b=22 первое разделим на 2
![a^{2} + b^{2}](https://tex.z-dn.net/?f=+a%5E%7B2%7D+%2B+b%5E%7B2%7D+)
= 61
Метод подстановки:
a=11-b =>
![(11-b)^{2} + b^{2}](https://tex.z-dn.net/?f=+%2811-b%29%5E%7B2%7D+%2B+b%5E%7B2%7D+)
= 61
121-22b+
![b^{2}](https://tex.z-dn.net/?f=+b%5E%7B2%7D+)
+
![b^{2}](https://tex.z-dn.net/?f=+b%5E%7B2%7D+)
=61
-22b+
![b^{2}](https://tex.z-dn.net/?f=+b%5E%7B2%7D+)
+
![b^{2}](https://tex.z-dn.net/?f=+b%5E%7B2%7D+)
= -60
-22b+2*
![b^{2}](https://tex.z-dn.net/?f=+b%5E%7B2%7D+)
+60=0 (кв. ур.)
D=484 - 480=4 =>
![\sqrt{D}](https://tex.z-dn.net/?f=+%5Csqrt%7BD%7D+)
= 2
b1=(22+2)/4=6 при b=6 a=5 S= 30
b2=(22-2)/4=5 при b=5 a=6 S=30
1)(x³+3x²)+(3x+9)=x²(x+3) + 3(x+3)=(x²+3)(x+3)
2)(x²-xy)-(2x-2y)=x(x-y)-2(x-y)=(x-2)(x-y)
3)m²+mn -(5m+5n)=m(m+n)-5(m+n)=(m-5)(m+n)
4)(a²-ab)-(3a-3b)=a(a-b)-3(a-b)=(a-3)(a-b)
5)(10ay-5by)+(2ax-bx)=5y(2a-b)+2x(a-b)=(5y+2x)(a-b)
6)(6by-15bx)-(4ay-10ax)=3b(2y-5x)-2a(2y-5x)=(3b-2a)(2y-5x)
7)5x(x-a)+7(x-a)=(5x+7)(x-a)
8)(4x²-4xz)-(3x-3z)=4x(x-z)-3(x-z)=(4x-3)(x-z)
9)5ax-5ay-(6bx-6by)=5a(x-y)-6b(x-y)=(5a-6b)(x-y)
10)(2m²-mn)+(2mx-nx)=m(2m-n)+x(2m-n)=(m+x)(2m-n)