Toán Cho x>y; x,y>0. Thỏa mãn x^2+3y^2=4xy Tính B= 2x+5y/x-2y 02/08/2021 By Sarah Cho x>y; x,y>0. Thỏa mãn x^2+3y^2=4xy Tính B= 2x+5y/x-2y
`x^2+3y^2=4xy` `<=> x^2 + 4y^2-2.2xy-y^2=0` `<=> (x – 2y)^2-y^2=0` `<=> ( x – 3y)(x – y)=0` `<=>` \(\left[ \begin{array}{l}x=3y\\x=y\end{array} \right.\) Mà ` x > y ; x , y > 0 ` Nên x = 3y => 2x = 6y Khi đó `B= (6y+5y)/(3y-2y)= (11y)/y=11` Trả lời
`x^2+3y^2=4xy`
`<=> x^2 + 4y^2-2.2xy-y^2=0`
`<=> (x – 2y)^2-y^2=0`
`<=> ( x – 3y)(x – y)=0`
`<=>` \(\left[ \begin{array}{l}x=3y\\x=y\end{array} \right.\)
Mà ` x > y ; x , y > 0 `
Nên x = 3y
=> 2x = 6y
Khi đó
`B= (6y+5y)/(3y-2y)= (11y)/y=11`