\(3a^2+3b^2=10ab\)

\(\Rightarrow3a^2-10ab+3b^2=0\)

\(\Rightarrow3a^2-ab-9ab+3b^2=0\)

\(\Rightarrow\left(3a^2-ab\right)-\left(9ab-3b^2\right)=0\)

\(\Rightarrow a\left(3a-b\right)-3b\left(3a-b\right)=0\)

\(\Rightarrow\left(3a-b\right)\left(a-3b\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}3a-b=0\\a-3b=0\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}b=-3a\\b=\dfrac{a}{3}\end{matrix}\right.\)

Với \(b=-3a,\)có :

\(P=\dfrac{-3a-a}{-3a+a}=\dfrac{-4a}{-2a}=2\)

Với \(b=\dfrac{a}{3},\)có :

\(P=\dfrac{\dfrac{a}{3}-a}{\dfrac{a}{3}+a}=\dfrac{\dfrac{a}{3}-\dfrac{3a}{3}}{\dfrac{a}{3}+\dfrac{3a}{3}}=\dfrac{-\dfrac{2a}{3}}{\dfrac{4a}{3}}=-\dfrac{2a}{3}.\dfrac{3}{4a}=-\dfrac{1}{2}\)

( Nếu sai thì cho mk xin lỗi nha bn , tại mk ko chắc lắm )

\(3a^2+3b^2=10ab\)

\(\Leftrightarrow3a^2-10ab+3b^2=0\)

\(\Rightarrow3a^2-9ab-ab+3b^2=0\)

\(\Leftrightarrow3a\left(a-3b\right)-b\left(a-3b\right)=0\)

\(\Leftrightarrow\left(a-3b\right)\left(3a-b\right)=0\)

Trường hợp 1: a=3b

\(A=\dfrac{a-b}{a+b}=\dfrac{3b-b}{3b+b}=\dfrac{2}{4}=\dfrac{1}{2}\)

Trường hợp 2: b=3a

\(A=\dfrac{a-b}{a+b}=\dfrac{a-3a}{a+3a}=\dfrac{-2}{4}=-\dfrac{1}{2}\)

ta có 3a² + 3b² = 10ab

=> 3a² + 3b² - 9ab-ab = 0          =>   ( 3a² - 9ab ) - ( ab - 3b^{2 )}  

=> ( a-3b ) (3a-b) = 0    => a=3b or  3a=b 

vì b>a>0  => 3a = b 

rùi bạn thay b bằng 3a rùi tính như thường thui

nhớ tick nghe chưa  k là k giải nữa đâu

Ta có : \(3a^2+3b^2=10ab\)

\(\Leftrightarrow\hept{\begin{cases}\left(a+b\right)^2=\frac{16ab}{2}\left(1\right)\\\left(a-b\right)^2=\frac{4ab}{3}\left(2\right)\end{cases}}\)

Lấy (1) chia (2) ta được:

\(\left(\frac{a+b}{a-b}\right)^2=6\Rightarrow\frac{a+b}{a-b}=\sqrt{6}\)

Ta có : \(3a^2+3b^2=10ab\Rightarrow3a^2+3b^2-10ab=0\)

\(\Rightarrow\left(4a^2-8ab+4a^2\right)-\left(a^2+2ab+b^2\right)=0\)

\(\Rightarrow\left(2a-2b\right)^2=\left(a+b\right)^2\Rightarrow2a-2b=a+b\Rightarrow a=3b\)

\(\Rightarrow D=\dfrac{a-b}{a+b}=\dfrac{3b-b}{3b+b}=\dfrac{1}{2}\)

\(3a^2+3b^2=10ab\)

\(\Leftrightarrow\left(3a^2-9ab\right)+\left(3b^2-ab\right)=0\)

\(\Leftrightarrow3a\left(a-3b\right)+b\left(3b-a\right)=0\)

\(\Leftrightarrow\left(a-3b\right)\left(3a-b\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}a=3b\\a=\dfrac{1}{3}b\end{matrix}\right.\)

Vì a>b>0 nên a=3b

\(\Rightarrow P=\dfrac{a-b}{a+b}=\dfrac{3b-b}{3b+b}=\dfrac{2b}{4b}=\dfrac{1}{2}\)

Ta có:

\(3a^2+3b^2=10ab\Leftrightarrow\left(3a-b\right)\left(a-3b\right)=0\Rightarrow a=3b\)

Xét: P² = \(\dfrac{\left(a-b\right)^2}{\left(a+b\right)^2}=\dfrac{a^2-2ab+b^2}{a^2+2ab+b^2}=\dfrac{3a^2+3b^2-6ab}{3a^2+3b^2+6ab}=\dfrac{10ab-6ab}{10ab+6ab}=\dfrac{4ab}{16ab}=\dfrac{1}{4}\)

=> P = \(\dfrac{1}{2}\)