2x + y = 7
( 1 / x ) + ( 1 / y ) = 5/6
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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