Выражения: 1) (x+2)(x-5)-3x(1-2x) 2) (a+3)(a-2)+(a-3)(a+6) 3) (x-7)(3x-+1)(2x-4) 4) (5x-2y)(3x+, 5x-3y)(4x+8y) 5) (3a²+5y)(2a³+y)-7a³(a²-3y)

Упростите выражения:
1) (x+2)(x-5)-3x(1-2x)
x^2-5x+2x-10-3x+6x^2=7x^2-6x-10

2) (a+3)(a-2)+(a-3)(a+6)
a^2-2a+3a-6+a^2+6a-3a-18=
2a^2+4a-24=a^2+2a-12

3) (x-7)(3x-2)-(5x+1)(2x-4)
3x^2-2x-21x+14-(10x^2-20x+2x-4)=
3x^2-23x+14-10x^2+18x-4=
-7x^2-5x+10

4) (5x-2y)(3x+5y)-(2,5x-3y)(4x+8y)
15x^2+25xy-6xy-10y^2-(10x^2+20xy-12xy-24y^2)=
15x^2+19xy-10y^2-10x^2-8xy+24y^2=
5x^2+14y^2+11xy

5) (3a²+5y)(2a³+y)-7a³(a²-3y)
6a^5+3a^2y+10a^3y+5y^2-7a^5+21a^3y=
-a^5+3a^2y+31a^3y+5y^2

Вот накалякал. Разбирайся :)

xy/(x+y) = 5
xz/(x+z) = 7
yz/(y+z) = 9

xy = 5x + 5y
xz = 7x + 7z
yz = 9y + 9z

x(y-5) = 5y
x = 5y/(y-5)

5yz/(y-5) = 35y/(y-5) + 7z
5yz = 35y + 7z * (y-5)
5yz = 35y + 7yz - 35z
2yz + 35y = 35z
y(2z + 35) = 35z
y = 35z/(2z + 35) = z/(2z/35 + 1)

35z^2/(2z + 35) = 315z/(2z + 35) + 9z
35z^2 = 315z + 9z*(2z + 35)
35z^2 = 315z + 18z^2 + 315z
17z^2 = 630z
z=630/17

y = 35*630/(2*630/17 + 35)/17 = 35*630/(1260 + 595) = 22050/1855 = 630 / 53

x = 5*630/(630/53 - 5)/53  =  5*630/((630/53 - 5)*53) = 5*630/365 = 630/73

Объяснение:

10)  5x²+3x-8=0;

a=5;   b=3;   c=-8;

D=b²-4ac=3²-4*5*(-8)=9+160=169>0   ---   2 корня.

x1=(-b+√D)/2a=(-3+√169)/2*5=( -3+13)/2*5=10/10=1;

x2=(-b-√D)/2a=(-3-√169)/2*5=(-3-13)/2*5=-16/10= -1.6.

***

7)  x²-4x+3=0;

По теореме Виета:

x1+x2=4;

x1*x2=3;

x1=3;  x2=1;

***

x²-2x-1=0;

a=1;   b=-2;   c= -1;

D=b²-4ac=(-2)²-4*1*(-1)=4+4=8>0 - 2 корня.

x1=(-(-2)+√8)/2*1=(2+2√2)/2 =1+√2;  

x2= (-(-2)-√8)/2=(2+2√2)/2=1-√2.  

***

9)  2x²-9x+10=0;

a=2;  b=-9;  c=10;

D=b²-4ac=(-9)²-4*2*10=81-80=1>0   ---   2 корня.

x1=(-b+√D)/2a=(-(-9)+√1)/2*2=10/4=2.5;

x2=(-b-√D)/2a=(-(-9)-√1)/2*2=(9-1)/4=8/4=2.