Số hạng đó là số hạng thứ 4 \(\Rightarrow k=3\) nên có dạng:

\(C_6^3\left(2x\right)^3.\left(-y^2\right)^3=-C_6^3\left(2x\right)^3y^6\)

Câu 6: 

a: \(\overrightarrow{AC}=\left(3;-3\right)\)

\(\overrightarrow{DB}=\left(4-x_D;1-y_D\right)\)

Để ACBD là hình bình hành thì \(\left\{{}\begin{matrix}4-x_D=3\\1-y_D=-3\end{matrix}\right.\Leftrightarrow D\left(1;4\right)\)

\(C=\dfrac{\sqrt{x}+1}{\sqrt{x}-1}-\dfrac{4\sqrt{x}}{x-1}\)

\(\Rightarrow C=\dfrac{\left(\sqrt{x}+1\right)^2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}-\dfrac{4\sqrt{x}}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)

\(\Rightarrow C=\dfrac{x+2\sqrt{x}+1-4\sqrt{x}}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)

\(\Rightarrow C=\dfrac{x-2\sqrt{x}+1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)

\(\Rightarrow C=\dfrac{\left(\sqrt{x}-1\right)^2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)

\(\Rightarrow C=\dfrac{\sqrt{x}-1}{\sqrt{x}+1}\)

Cho mik hỏi tại sao ra \(X+2\sqrt{X}+1\)mà ko phải \(2\sqrt{X}+1\)

`a)A` có nghĩa `<=>x-1 >= 0 <=>x >= 1`

`b)B=\sqrt{3^2 .2}+\sqrt{2^3}-\sqrt{5^2 .2}`

`<=>B=3\sqrt{2}+2\sqrt{2}-5\sqrt{2}`

`<=>B=0`

`c)` Với `a >= 0,a \ne 1` có:

`C=[a-1]/[\sqrt{a}-1]-[a\sqrt{a}-1]/[a-1]`

`C=[(a-1)(\sqrt{a}+1)-a\sqrt{a}+1]/[(\sqrt{a}-1)(\sqrt{a}+1)]`

`C=[a\sqrt{a}+a-\sqrt{a}-1-a\sqrt{a}+1]/[(\sqrt{a}-1)(\sqrt{a}+1)]`

`C=a/[a-1]`

bài 2 nào ạ

Bài 2:

\(a.\left(5-a\right)\sqrt{\dfrac{8a}{a-5}}\\ a>5 \\= \sqrt{\dfrac{8a\left(5-a\right)^2}{a-5}}\\ =\sqrt{\dfrac{8a\left(a-5\right)^2}{a-5}}\\ =\sqrt{8a\left(a-5\right)}=\sqrt{8a^2-40}\\b.\left(x-7\right)\sqrt{\dfrac{\left(x+7\right)}{49-x^2}}\\ =\left(x-7\right)\sqrt{\dfrac{\left(x+7\right)}{\left(7-x\right)\left(x+7\right)}}\\ \left(x-7\right)\sqrt{\dfrac{1}{7-x}}\\ =\sqrt{\dfrac{\left(x-7\right)^2}{7-x}}=\sqrt{\dfrac{\left(7-x\right)^2}{7-x}}\\ =\sqrt{7-x}\\ c.\)

\(\dfrac{a}{b}\sqrt{\dfrac{b}{a}}\\ a,b>0 \\ =\sqrt{\dfrac{a^2b}{b^2a}}=\sqrt{\dfrac{a}{b}}\\ d.x\sqrt{\dfrac{6}{x}}\\ x>0\\ =\sqrt{\dfrac{6x^2}{x}}=\sqrt{6x}\)

Bài 3:

\(a.7\sqrt{2}=\sqrt{7^2.2}=\sqrt{98}\)

Vì \(\sqrt{98}>\sqrt{72}\Rightarrow7\sqrt{2}>\sqrt{72}\)

\(b.4\sqrt[]{3}=\sqrt{4^2.3}=\sqrt{48}\\ 3\sqrt{5}=\sqrt{3^2.5}=\sqrt{45}\)

vì: \(48>45\Rightarrow\sqrt{48}>\sqrt{45}\Rightarrow4\sqrt{3}>3\sqrt{5}\)

c.\(4\sqrt{7}=\sqrt{4^2.7}=\sqrt{112}\\ 5\sqrt{6}=\sqrt{5^2.6}=\sqrt{150}\)

Vì: \(112< 150\Rightarrow\sqrt{112}< \sqrt{150}\Rightarrow4\sqrt{7}< 5\sqrt{6}\)

d.\(\dfrac{1}{6}\sqrt{18}=\sqrt{\dfrac{18}{6^2}}=\sqrt{\dfrac{18}{36}}=\sqrt{\dfrac{1}{2}}\\ \dfrac{1}{2}\sqrt{2}=\sqrt{\dfrac{2}{4}}=\sqrt{\dfrac{1}{2}}\)

Vì: \(\dfrac{1}{2}=\dfrac{1}{2}\Rightarrow\sqrt{\dfrac{1}{2}}=\sqrt{\dfrac{1}{2}}\Rightarrow\dfrac{1}{6}\sqrt{15}=\dfrac{1}{2}\sqrt{2}\)

Bài 4: 

a: Xét ΔOBN vuông tại B và ΔOAM vuông tại A có

OB=OA

\(\widehat{O}\) chung

Do đó: ΔOBN=ΔOAM

Suy ra: BN=AM; ON=OM; \(\widehat{N}=\widehat{M}\)

Xét ΔKAN vuông tại A và ΔKBM vuông tại K có 

AN=BM

\(\widehat{N}=\widehat{M}\)

Do đó: ΔKAN=ΔKBM

b: Xét ΔOKN và ΔOKM có 

OK chung

KN=KM

ON=OM

Do đó: ΔOKN=ΔOKM

Suy ra: \(\widehat{KOM}=\widehat{KON}\)

hay OK là tia phân giác của góc MAN

1.Quan went to the doctor because he had a headache.

2.Tam was beautiful and gentle.

Quan went to the doctor because he had a headache