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\(2\sqrt{24}-9\sqrt{\frac{2}{3}}+\frac{\sqrt{6}-6}{\sqrt{6}}\)
\(=2\sqrt{4}.\sqrt{6}-\frac{9.\sqrt{6}}{3}+\frac{\sqrt{6}\left(1-\sqrt{6}\right)}{\sqrt{6}}\)
\(=4\sqrt{6}-3\sqrt{6}+1-\sqrt{6}\)
\(=1\)
\(\frac{5\sqrt{3}-3\sqrt{5}}{\sqrt{5}-\sqrt{3}}+\frac{1}{4+\sqrt{15}}\)
\(\frac{a\sqrt{a}+b\sqrt{b}}{\sqrt{a}+\sqrt{b}}-\sqrt{ab}=\frac{\sqrt{a^3}+\sqrt{b^3}}{\sqrt{a}+\sqrt{b}}-\sqrt{ab}\)
\(=\frac{\left(\sqrt{a}+\sqrt{b}\right)\left(a-\sqrt{ab}+b\right)}{\sqrt{a}+\sqrt{b}}-\sqrt{ab}\)
\(=a-\sqrt{ab}+b-\sqrt{ab}\)
\(=\left(\sqrt{a}-\sqrt{b}\right)^2\)
Anh ko ghi lại đề nha bé
\(\Leftrightarrow\hept{\begin{cases}\frac{27x-14y}{21}=-\frac{28}{21}\\\frac{15x+24y}{10}=\frac{15}{10}\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}27x-14y=-28\\15x+24y=15\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}324x-168y=-336\\105x+168y=105\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}429x=-231\\15x+24y=15\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}x=-\frac{7}{13}\\y=\frac{15-15x}{24}\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}x=-\frac{7}{13}\\y=\frac{15-15.\left(-\frac{7}{13}\right)}{24}\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}x=-\frac{7}{13}\\y=\frac{25}{26}\end{cases}}\)
\(P=x^2y^2+1+1+\frac{1}{x^2y^2}=x^2y^2+2+\frac{1}{256x^2y^2}+\frac{255}{256x^2y^2}\)
\(\ge x^2y^2+\frac{1}{256x^2y^2}+2+\frac{255}{256.\left[\frac{\left(x+y\right)^2}{4}\right]^2}\ge2\sqrt{x^2y^2.\frac{1}{256x^2y^2}}+2+\frac{255}{256.\frac{1}{16}}\)
\(=\frac{1}{8}+2+\frac{255}{16}=\frac{289}{16}\)
Dấu "=" xảy ra khi \(x=y=\frac{1}{2}\)
\(4x^2-y^2=3\Leftrightarrow y^2=4x^2-3\)
\(\Rightarrow3x^2+4x^2-3=2\)
\(7x^2=5\)
\(x^2=\frac{5}{7}\)
\(x\in\left\{\pm\sqrt{\frac{5}{7}}\right\}\)
Xét các t/h của x rồi tìm y xong kết luận nhé
3x2 + y2 =2 (1)
4x2 -Y2 = 3 (2)
Cộng 1 và 2 ta có
3x2 + 4x2 = 5
x2(3+4) = 5
x2 = 5/7
x= tu tinh
thay x vao 1 tim y
ok!
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a,Gọi H là giao điểm OA với BC
Vì OB = OC ( bán kính (O) )
AB = AC ( tiếp tuyến )
=> AO là trung trực của BC
=> AO vuông góc với BC tại H
Xét \(\(\Delta\)\)OAB vuông tại B có BH là đường cao
\(\(OB^2=OH.OA\)\)
Mà OB = OD (bán kính)
\(\(\Rightarrow OH.OA=OD^2\)\)
Từ \(\(OH.OA=OD^2\)\)
\(\(\Rightarrow\)\)\(\(\frac{OD}{OH}=\frac{OA}{OD}\)\)
Xét \(\(\Delta\)\)OHD và \(\(\Delta\)\)ODA có
\(\(\frac{OD}{OH}=\frac{OA}{OD}\left(cmt\right)\)\)
^DOA chung
\(\(\Rightarrow\Delta OHD~\Delta ODA\left(c.g.c\right)\)\)
b,Xét \(\(\Delta\)\)ABD và \(\(\Delta\)\)AEB có :
^BAE chung
^BEA = ^DBA ( cùng chắn cung BD)
=> \(\(\Delta ABD~\Delta AEB\left(g.g\right)\)\)
Có cách nào chứng minh Góc BEA=góc DBA ko? Chắn cung mình chưa học