\(gọi:AB=x;AC=y\)
\(có:x^2+y^2-2xy.cos135^o=BC^2=25\left(1\right)\)
\(\dfrac{BC}{sin135^o}=5\sqrt{2}=\dfrac{x}{sinC}=\dfrac{y}{sinB}\Leftrightarrow\dfrac{x}{\dfrac{AH}{y}}+\dfrac{y}{\dfrac{AH}{x}}=5\sqrt{2}\Leftrightarrow2xy=5\sqrt{2}\left(2\right)\)
\(\)\(\left(1\right)\left(2\right)\Rightarrow\left\{{}\begin{matrix}x^2+y^2-2xycos135^o=25\Leftrightarrow\left(x+y\right)^2-2xy-2xycos135^2=25\\2xy=5\sqrt{2}\end{matrix}\right.\)
giải bằng cách đặt \(\left\{{}\begin{matrix}S=x+y\\P=xy\end{matrix}\right.\)\(\left(S^2\ge4P\right)\)
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