Question

[Cao Hoài Phúc]

1.cho phan thuc P=\(\frac{5x-4y}{5x+4y}\)voi 25x²+16y²=50xy.khi do gia tri cua bieu thuc P=\(\frac{1+P^2}{1-P^2}\)la

2.gia tri lon nhat cua bieu thuc B=\(\frac{14}{\frac{x^2}{4}-3x+16}la\)

3.gia tri cua a de da thuc A=2x³+7x²+ax+3 chia het cho B=(x+1)²la a=?

Answer 1

[Phước Nguyễn]

\(25x^2+16y^2=50xy\)

\(\Leftrightarrow\) \(\left(5x+4y\right)^2-40xy=50xy\)

\(\Leftrightarrow\) \(\left(5x+4y\right)^2=90xy\)

Mặt khác, ta cũng có:  \(25x^2+16y^2=50xy\)

\(\Leftrightarrow\)  \(\left(5x-4y\right)^2=10xy\)

Do đó:

\(P^2=\frac{\left(5x-4y\right)^2}{\left(5x+4y\right)^2}=\frac{10xy}{90xy}=\frac{1}{9}\)

Vậy,  \(P'=\frac{1+\frac{1}{9}}{1-\frac{1}{9}}=1\frac{1}{4}\)

Answer 2

[Nguyễn Nhật Minh]

1)

 \(25x^2-40xy+16y^2=10xy\Leftrightarrow\left(5x-4y\right)^2=10xy\)

\(25x^2+40xy+16y^2=10xy\Leftrightarrow\left(5x+4y\right)^2=90xy\)

\(P^2=\frac{1}{9}\Leftrightarrow Q=\frac{1+P^2}{1-P^2}=\frac{1+\frac{1}{81}}{1-\frac{1}{81}}=\frac{82}{80}=\frac{41}{40}\)