Question

Answer 1

Bài 1:

\(a,=12\sqrt{3}-15\sqrt{3}+8\sqrt{3}=5\sqrt{3}\\ b,=2\sqrt{3}-1-\sqrt{\left(\sqrt{3}+1\right)^2}=2\sqrt{3}-1-\sqrt{3}-1=\sqrt{3}-2\)

Bài 2:

\(A=\dfrac{a-4\sqrt{a}+4-a-4\sqrt{a}-4}{\left(\sqrt{a}-2\right)\left(\sqrt{a}+2\right)}\cdot\dfrac{\left(\sqrt{a}-2\right)\left(\sqrt{a}+2\right)}{\sqrt{a}}=\dfrac{-8\sqrt{a}}{\sqrt{a}}=-8\left(đpcm\right)\)

Answer 2

Bài 5:

\(ĐK:x\ge1;y\ge4\\ \Leftrightarrow M=\dfrac{y\sqrt{1\left(x-1\right)}+\dfrac{1}{2}x\sqrt{4\left(y-4\right)}}{xy}\le\dfrac{\dfrac{y\left(x-1+1\right)}{2}+\dfrac{1}{2}\cdot\dfrac{x\left(y-4+4\right)}{2}}{xy}=\dfrac{\dfrac{xy}{2}+\dfrac{xy}{4}}{xy}=\dfrac{3xy}{4xy}=\dfrac{3}{4}\)

Dấu \("="\Leftrightarrow\left\{{}\begin{matrix}x-1=1\\y-4=4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2\\y=8\end{matrix}\right.\)