a) \(A=\left(\frac{1}{a-\sqrt{a}}+\frac{1}{\sqrt{a}-1}\right):\frac{\sqrt{a}+1}{a-2\sqrt{a}+1}\left(a>0;a\ne1\right)\)

\(=\left[\frac{1}{\sqrt{a}\left(\sqrt{a}-1\right)}+\frac{1}{\sqrt{a}-1}\right]:\frac{\sqrt{a}+1}{\left(\sqrt{a}-1\right)^2}\)

\(=\frac{1+\sqrt{a}}{\sqrt{a}\left(\sqrt{a}-1\right)}\cdot\frac{\left(\sqrt{a}-1\right)^2}{\sqrt{a}+1}\)

\(=\frac{\sqrt{a}-1}{\sqrt{a}}\)

b) Để \(A=\frac{1}{2}\)

\(\Leftrightarrow\frac{\sqrt{a}-1}{\sqrt{a}}=\frac{1}{2}\)

\(\Leftrightarrow2\sqrt{a}-2=\sqrt{a}\)

\(\Leftrightarrow\sqrt{a}=2\Leftrightarrow a=4\left(tm\right)\)

sai đề phần a)

lần đầu thấy tứ giác có 3 đỉnh

x + 2/5 = 2-x/4 

=>20x /20 + 8 /20 = 40 /20 -5x /20 

=>20x+8 = 40 -5x 

=>20x +8 -40 +5x =0 

=>25x -32 =0

=>x=32/25 

Ví dụ a/b = c/d

=> a.c = b.d

a.d ( là tích ngoại tỉ )

b.c ( là tích trung tỉ )

a) Có: \(\left(a-1\right)^2\ge0,\forall a\)

\(\Leftrightarrow a^2-2a+1\ge0\)

\(\Leftrightarrow a^2+2a+1\ge4a\)

\(\Leftrightarrow\left(a+1\right)^2\ge4a\)

=>đpcm

b) Áp dụng bđt trên ta có:

\(\left(a+1\right)^2\ge4a\) (1)

\(\left(b+1\right)^2\ge4b\) (2)

\(\left(c+1\right)^2\ge4c\) (3)

Nhân vế vs vế (1) ; (2);(3) ta đc:

\(\left(a+1\right)^2\left(b+1\right)^2\left(c+1\right)^2\ge4a\cdot4b\cdot4c=64abc=64\)

\(\Rightarrow\left(a+1\right)\left(b+1\right)\left(c+1\right)\ge8\)

a) Xét ΔAKB và ΔAKC có:

AB=AC(gt)

AK:cạnh chung

BK=CK(gt)

=> ΔAKB=ΔAKC(c.c.c)

=> \(\widehat{AKB}=\widehat{AKC}\)

Mà: \(\widehat{AKB}+\widehat{AKC}=180^o\)

=> \(\widehat{AKB}=\widehat{AKC}=90^o\)

=> \(AK\perp BC\)

b) Vì: \(EC\perp BC\left(gt\right)\)

Mad: \(AK\perp BC\left(cmt\right)\)

=> EC//AK

a) Xét ΔABN và ΔACM có:

AB=AC(gt)

\(\widehat{A}\) : góc chung

AN=AM(gt)

=> ΔABN=ΔACM(c.g.c)

=> \(\widehat{B_1}=\widehat{C_1}\)

Vì: ΔABC cân tại A(gt)

=> \(\widehat{B}=\widehat{C}\)

Vì: \(\widehat{B}=\widehat{B_1}+\widehat{B_2}\)

\(\widehat{C}=\widehat{C_1}+\widehat{C_2}\)

Mà: \(\widehat{B}=\widehat{C}\left(cmt\right);\widehat{B_1}=\widehat{C_1}\left(cmt\right)\)

=> \(\widehat{B_2}=\widehat{C_2}\)

=> ΔBIC cân tại I

\(\left(2x-14\right)\left(3^x-9\right)=0\)

\(\Leftrightarrow\left[\begin{array}{nghiempt}2x-14=0\\3^x-9=0\end{array}\right.\)\(\Leftrightarrow\left[\begin{array}{nghiempt}2x=14\\3^x=9\end{array}\right.\)

\(\Leftrightarrow\left[\begin{array}{nghiempt}x=7\\x=2\end{array}\right.\)

=(3x^3-5x^3)-(6x-3x)

=-2x^3-3x