( x / y ) + ( y / x ) = 10/3
x + y = 8
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( x² + y² ) / xy = 10/3
3( x² + y² ) = 10xy
3x² + 3y² = 10xy
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y = 8 - x
3x² + 3( 8 - x )² = 10x( 8 - x )
3x² + 3( 64 - 16x + x² ) = 80x - 10x²
3x² + 192 - 48x + 3x² = 80x - 10x²
6x² - 48x + 192 - 80x + 10x² = 0
16x² - 128x + 192 = 0
16( x² - 8x + 12 ) = 0
D = 64 - 48 = 16 = 4²
x1 = ( 8 + 4 ) : 2 = 6
x2 = ( 8 - 4 ) : 2 = 2
y1 = 8 - 6 = 2
y2 = 8 - 2 = 6
Ответ ( 6 ; 2 ) ; ( 2 ; 6 )