a: Xét tứ giác BAOD có 

\(\widehat{BAO}+\widehat{BDO}=180^0\)

Do đó: BAOD là tứ giác nội tiếp

\(a,\Leftrightarrow m+1=-2\Leftrightarrow m=-3\\ \text{Vì }-3< 0\text{ nên hàm số nghịch biến}\)

4.

a, \(A=\sqrt[3]{15\sqrt{3}+26}=\sqrt[3]{\left(\sqrt{3}+2\right)^3}=\sqrt{3}+2\)

b, \(B=\sqrt[3]{5+2\sqrt{13}}+\sqrt[3]{5-2\sqrt{13}}\)

\(\Rightarrow2B=\sqrt[3]{40+16\sqrt{13}}+\sqrt[3]{40-16\sqrt{13}}\)

\(=\sqrt[3]{\left(\sqrt{13}+1\right)^3}+\sqrt[3]{\left(\sqrt{13}-1\right)^3}\)

\(=\sqrt{13}+1+\sqrt{13}-1=2\sqrt{13}\)

\(\Rightarrow B=\sqrt{13}\)

c, \(C=\sqrt[3]{182-\sqrt{33125}}+\sqrt[3]{182+\sqrt{33125}}\)

\(\Rightarrow C^3=364+3\sqrt[3]{182-\sqrt{33125}}.\sqrt[3]{182+\sqrt{33125}}\left(\sqrt[3]{182-\sqrt{33125}}+\sqrt[3]{182+\sqrt{33125}}\right)\)

\(=364-3C\)

\(\Rightarrow C^3+3C-364=0\)

\(\Leftrightarrow C=7\)

Câu 1

a)=\(8\sqrt{3}-10\sqrt{3}+15\sqrt{3}=13\sqrt{3}\)

b)=\(4\sqrt{x}+6\sqrt{x}-6\sqrt{x}=4\sqrt{x}\)

c)=\(21\sqrt{2}+8\sqrt{2}-28\sqrt{2}=\sqrt{2}\)

d)\(\Rightarrow\)\(8\sqrt{2\sqrt{3}}-\sqrt{5\sqrt{3}}-4\sqrt{5\sqrt{3}}\)

\(\Rightarrow\)\(8\sqrt{2\sqrt{3}}-5\sqrt{5\sqrt{3}}\)

câu 2

a)\(\Rightarrow4x=64\)\(\Rightarrow x=16\)

b)\(\Rightarrow9x\le36\)\(\Rightarrow x\le4\)

Câu 2: 

a: Ta có: \(\sqrt{4x}=8\)

\(\Leftrightarrow4x=64\)

hay x=16

b: Ta có: \(\sqrt{9x}\le6\)

\(\Leftrightarrow9x\le36\)

\(\Leftrightarrow x\le4\)

Kết hợp ĐKXĐ, ta được: \(0\le x\le4\)

a) Ta có: \(P=\dfrac{a\sqrt{a}-1}{a-\sqrt{a}}-\dfrac{a\sqrt{a}+1}{a+\sqrt{a}}+\left(\sqrt{a}-\dfrac{1}{\sqrt{a}}\right)\left(\dfrac{3\sqrt{a}}{\sqrt{a}-1}-\dfrac{\sqrt{a}+2}{\sqrt{a}+1}\right)\)

\(=\dfrac{\left(\sqrt{a}-1\right)\left(a+\sqrt{a}+1\right)}{\sqrt{a}\left(\sqrt{a}-1\right)}-\dfrac{\left(\sqrt{a}+1\right)\left(a-\sqrt{a}+1\right)}{\sqrt{a}\left(\sqrt{a}+1\right)}+\dfrac{a-1}{\sqrt{a}}\cdot\dfrac{3\sqrt{a}\left(\sqrt{a}+1\right)-\left(\sqrt{a}+2\right)\left(\sqrt{a}-1\right)}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}\)

\(=\dfrac{a+\sqrt{a}+1-a+\sqrt{a}-1}{\sqrt{a}}+\dfrac{3a+3\sqrt{a}-\left(a-\sqrt{a}+2\sqrt{a}-2\right)}{\sqrt{a}}\)

\(=2+\dfrac{3a+3\sqrt{a}-a+\sqrt{a}-2\sqrt{a}+2}{\sqrt{a}}\)

\(=\dfrac{2\sqrt{a}+2a+2\sqrt{a}+2}{\sqrt{a}}\)

\(=\dfrac{2\left(a+2\sqrt{a}+1\right)}{\sqrt{a}}\)

\(=\dfrac{2\left(\sqrt{a}+1\right)^2}{\sqrt{a}}\)

b) Ta có: \(P-6=\dfrac{2\left(\sqrt{a}+1\right)^2-6\sqrt{a}}{\sqrt{a}}\)

\(=\dfrac{2a+4\sqrt{a}+2-6\sqrt{a}}{\sqrt{a}}\)

\(=\dfrac{2\left(a-\sqrt{a}+1\right)}{\sqrt{a}}>0\forall a\) thỏa mãn ĐKXĐ

hay P>6

Câu 1:

1) Ta có: \(2x^2+5x-3=0\)

\(\Leftrightarrow2x^2+6x-x-3=0\)

\(\Leftrightarrow\left(x+3\right)\left(2x-1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-3\\x=\dfrac{1}{2}\end{matrix}\right.\)

2) Để hàm số đồng biến trên R thì m-1>0

hay m>1

Câu 1: 

3) Ta có: P=a+b-2ab

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

\(=2-2\cdot\left(-1\right)=4\)