\(\sqrt{\left(\sqrt{2}+\sqrt{3}+1\right)^2-\sqrt{\left(\sqrt{2}+\sqrt{3}\right)^2}}\)

\(=\sqrt{\sqrt{2}+\sqrt{3}+1-\sqrt{2}-\sqrt{3}}=1\)

sr nha tại lâu rùi nay cj ms onl nên ko rep kịp

\(\sqrt{2-x}=3-\sqrt{3x+1}\left(ĐK:-\frac{1}{3}\le x\le2\right)\)

\(\Leftrightarrow\sqrt{2-x}+\sqrt{3x+1}=3\)

\(\Leftrightarrow2-x+3x+1+2\sqrt{\left(2-x\right)\left(3x-1\right)}=9\)

\(\Leftrightarrow2\sqrt{\left(2-x\right)\left(3x+1\right)}=6-2x\)

\(\Leftrightarrow\sqrt{\left(2-x\right)\left(3x+1\right)}=3-x\left(ĐK:x\le3\right)\)

\(\Leftrightarrow\left(2-x\right)\left(3x+1\right)=9-6x+x^2\)

\(\Leftrightarrow6x+2-3x^2-x=9-6x+x^2\)

\(\Leftrightarrow4x^2-1x+7=0\)

\(\Leftrightarrow\left(4x-7\right)\left(x-1\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x=\frac{7}{4}\left(t/m\right)\\x=1\left(t/m\right)\end{cases}}\)

Vậy pt đã cho có nghiệm \(S=\left\{\frac{7}{4};1\right\}\)

Chúc bạn học tốt !!!

M E K H G I F

a ) Xét \(\Delta KFH\) và \(\Delta KEF\) có :

\(\widehat{K}\) chung ; \(\widehat{KFH}=\widehat{KEF}=\left(\frac{1}{2}sđcungHF\right)\)

\(\Rightarrow\Delta KFH\) đồng dạng \(\Delta KEF\)

\(\Rightarrow KF^2=KE.KH\left(1\right)\)

b) Vì : EG//MF (gt) \(\Rightarrow\widehat{KMH}=\widehat{MGE}\)

Mà : \(\widehat{MGE}=\widehat{MEH}=\left(\frac{1}{2}sđcungHE\right)\)

\(\Rightarrow\widehat{KMH}=\widehat{MEH}\)

\(\Rightarrow\Delta KHM\) đồng dạng \(\Delta KME\)

\(\Rightarrow\frac{KM}{KE}=\frac{KH}{KM}\Rightarrow KM^2=KE.KH\left(2\right)\)

Từ (1) và (2) \(\Rightarrow\) đpcm

Chúc bạn học tốt !!!