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\(a^2-3ab+2b^2=0\)
\(\Leftrightarrow a^2-2ab-ab+2b^2=0\)
\(\Leftrightarrow a\left(a-2b\right)-b\left(a-2b\right)=0\)
\(\Leftrightarrow\left(a-2b\right)\left(a-b\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}a=2b\\a=b\end{matrix}\right.\)
+) TH1: \(a=2b\)
\(P=\frac{a+2b}{3a}+\frac{b+2a}{3b}\)
\(P=\frac{2b+2b}{6b}+\frac{b+4b}{3b}\)
\(P=\frac{4b}{6b}+\frac{5b}{3b}\)
\(P=\frac{4}{6}+\frac{5}{3}=\frac{7}{3}\)
+) TH2: \(a=b\)
\(P=\frac{a+2b}{3a}+\frac{b+2a}{3b}\)
\(P=\frac{3a}{3a}+\frac{3b}{3b}=1+1=2\)
Vậy....
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\(2a^2+b^2=3ab\Leftrightarrow2a^2-3ab+b^2=0\Leftrightarrow\left(2a-b\right)\left(a-b\right)=0\)
\(\Leftrightarrow a-b=0\left(2a-b>0\right)\Leftrightarrow a=b\)
\(P=\frac{3a^2+2a^2}{5a^2-3a^2}=\frac{5a^2}{2a^2}=\frac{5}{2}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
cách khác:
\(B=\frac{3a-2b}{2a+5}+\frac{3b-a}{b-5}\)
\(=\frac{3a-2b}{2a+a-2b}+\frac{3b-a}{b-a+2b}\) (thay 5 = a - 2b)
\(=\frac{3a-2b}{3a-2b}+\frac{3b-a}{3b-a}\)
\(=1+1=2\)
Biết a - 2b = 5 tính giá trị biểu thức:
\(B=\frac{3a-2b}{2a+5}+\frac{3b-a}{b-5}\)
\(=\frac{2a+\left(a-2b\right)}{2a+5}+\frac{3b-a}{b-5}\)
\(=\frac{2a+5}{2a+5}+\frac{b-5}{b-5}\)
\(=1+1=2\)
Vậy B = 2
![](https://rs.olm.vn/images/avt/0.png?1311)
a-2b=5 => a=2b+5
Thay a=2b+5 vào B thì :
B = 6b+15-2b/4b+10+5 + 3b-2b-5/b-5
= 4b+15/4b+15 + b-5/b-5 = 1+1 = 2
Tk mk nha
Ta có : a - 2b = 5 \(\Rightarrow\)2b = a - 5
a - 2b = 5 \(\Rightarrow\)a = 2b + 5
Thay vào , ta được :
\(B=\frac{3a-\left(a-5\right)}{2a+5}+\frac{3b-\left(2b+5\right)}{b-5}\)
\(B=\frac{3a-a+5}{2a+5}+\frac{3b-2b-5}{b-5}\)
\(B=\frac{2a+5}{2a+5}+\frac{b-5}{b-5}\)
\(B=1+1=2\)
\(a^2-3ab+2b^2=0\)
\(\Leftrightarrow a^2-2ab-ab+2b^2=0\)
\(\Leftrightarrow a\left(a-2b\right)-b\left(a-2b\right)=0\)
\(\Leftrightarrow\left(a-2b\right)\left(a-b\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}a=2b\\a=b\end{cases}}\)
+ ) TH1 :
\(a=2b\)
\(P=\frac{a+2b}{3a}+\frac{b+2a}{3b}\)
\(P=\frac{2b+2b}{6b}+\frac{b+4b}{3b}\)
\(P=\frac{4b}{6b}+\frac{5b}{3b}\)
\(P=\frac{4}{6}+\frac{5}{3}=\frac{7}{3}\)
+ ) TH 2 \(a=b\)
\(P=\frac{a+2b}{3a}+\frac{b+2a}{3b}\)
\(P=\frac{3a}{3a}+\frac{3b}{3b}=1+1=2\)
Chúc bạn học tốt !!!