Question

Cho a,b thỏa mãn :a^2+b^2+5=2a+4b.Tính giá trị P=|2a-3b|+a+5

 

Answer 1

Ta có:a²+b²+5=2a+4b

   ⇔  (a²-2a+1)+(b²-4b+4)=0

   ⇔  (a-1)²+(b-2)²=0

\(\Leftrightarrow\left\{{}\begin{matrix}\left(a-1\right)^2=0\\\left(b-2\right)^2=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}a=1\\b=2\end{matrix}\right.\)

Thay vào P ta có:

 \(P=\left|2.1-3.2\right|+1+5=10\)