Question

решить систему уравнений

Answer 1

2x + y = 7
( 1 / x ) + ( 1 / y ) = 5/6 
------------------------------
y = 7 - 2x 
( y + x ) / xy = 5/6 
x ≠ 0 ; y ≠ 0
6x + 6y = 5xy 
6x + 6( 7 - 2x ) =  5x( 7 - 2x )
6x + 42 - 12x = 35x - 10x^2
10x^2 - 41x + 42 = 0
x1 = ( 41 - 1 ) : 20 = 2 
x2 = ( 41 + 1 ) : 20 = 2,1 
y1 = 7 - 4 = 3 
y2 = 7 - 4,2 = 2,8 
Ответ ( 2 ; 3 ) ; ( 2,1 ; 2,8 ) 
Проверка 
1) 2*2 + 3 = 7 ⇒ 7 = 7 
2) 2*2,1 + 2,8 = 7 ⇒ 7 = 7
3) 1/2 + 1/3 = 5/6 ⇒ 3/6 + 2/6 = 5/6 ⇒ 5/6 = 5/6
4) ( 1 : 2,1 ) + ( 1 : 2,8 ) = 5/6
1 : ( 21/10 ) + 1 : ( 28/10 ) = 5/6
10/21 + 10/28 = 5/6
10/21 + 5/14 = 5/6
20/42 + 15/42 = 35/42 
35/42 = 35/42 

Answer 2

{2x+y=7⇒y=7-2x
{1/x+1/y=5/6⇒6x+6y=5xy
6x+6(7-2x)=5x(7-2x)
6x+42-12x=35x-10x²
10x²-41x+42=0
D=1681-1680=1
x1=(41-1)/20=2⇒y1=7-4=3
x2=(41+1)/20=2,1⇒y2=(7-4,2=2,8
(2;3);(2,1;2,8)