Question

3.已知实数xyz满足+3/(x+y)=4/(y+z)=5/(2+x)+则+(6y-7x)/(2)^2+y-6x+的值为+(

Answer 1

问：3.已知实数xyz满足+3/(x+y)=4/(y+z)=5/(2+x)+则+(6y-7x)/(2)^2+y-6x+的值为+(

答：根据等比例中线定理，有：3/(x+y) = 4/(y+z) => 3y + 3z = 4x + 4y => z = (4/3)x4/(y+z) = 5/(2+x) => 4x + 4y = 5y + 5z => x = (1/5)y + (1/5)z代入z的表达式，得到：x = (7/15)x + (4/9)y移项化简得：(6y-7x)/(2)^2+y-6x = (6y - 7[(2/9)x + (4/9)y])/(2 + y - (2/3)x)再代入x的表达式：(6y-7x)/(2)^2+y-6x = (6y - 7[(2/9)(1/5)y + (2/9)(4/3)x])/(2 + y - (2/3)x)化简得：(6y-7x)/(2)^2+y-6x = (2/9)y因此，(6y-7x)/(2)^2+y-6x的值为(2/9)y。