a, \(\dfrac{2^3-x^3}{x\left(x^2+2x+4\right)}\) = \(\dfrac{\left(2-x\right)\left(x^2+2x+4\right)}{x\left(x^2+2x+4\right)}\) = \(\dfrac{2-x}{x}\)=\(\dfrac{x-2}{-x}\)(đpcm)

b, \(\dfrac{-3x\left(x-y\right)}{y^2-x^2}\) (\(x\) \(\ne\) \(\pm\) y)

= \(\dfrac{-3x\left(x-y\right)}{\left(y-x\right)\left(y+x\right)}\)

= \(\dfrac{3x\left(y-x\right)}{\left(y-x\right)\left(y+x\right)}\)

= \(\dfrac{3x}{x+y}\) (đpcm)

c, \(\dfrac{3a\left(x+y\right)^2}{9a^2\left(x+y\right)}\) (đk a \(\ne\)0; \(x\) \(\ne\) - y)

   = \(\dfrac{3.a.\left(x+y\right)\left(x+y\right)}{3.3.a.a.\left(x+y\right)}\)

   =    \(\dfrac{x+y}{3a}\) (đpcm)

\(1,ĐK:x\ge2\\ PT\Leftrightarrow\sqrt{3x-6}+x-2-\left(\sqrt{2x-3}-1\right)=0\\ \Leftrightarrow\dfrac{3\left(x-2\right)}{\sqrt{3x-6}}+\left(x-2\right)-\dfrac{2\left(x-2\right)}{\sqrt{2x-3}+1}=0\\ \Leftrightarrow\left(x-2\right)\left(\dfrac{3}{\sqrt{3x-6}}-\dfrac{2}{\sqrt{2x-3}+1}+1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=2\left(tm\right)\\\dfrac{3}{\sqrt{3x-6}}-\dfrac{2}{\sqrt{2x-3}+1}+1=0\left(1\right)\end{matrix}\right.\)

Với \(x>2\Leftrightarrow-\dfrac{2}{\sqrt{2x-3}+1}>-\dfrac{2}{1+1}=-1\left(3x-6\ne0\right)\)

\(\Leftrightarrow\left(1\right)>0-1+1=0\left(vn\right)\)

Vậy \(x=2\)

\(2,ĐK:x\ge-1\)

Đặt \(\left\{{}\begin{matrix}\sqrt{x+1}=a\\\sqrt{x^2-x+1}=b\end{matrix}\right.\left(a,b\ge0\right)\Leftrightarrow a^2+b^2=x^2+2\)

\(PT\Leftrightarrow2a^2+2b^2-5ab=0\\ \Leftrightarrow\left(a-2b\right)\left(2a-b\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}a=2b\\b=2a\end{matrix}\right.\)

Với \(a=2b\Leftrightarrow x+1=4x^2-4x+4\left(vn\right)\)

Với \(b=2a\Leftrightarrow4x+4=x^2-x+1\Leftrightarrow x^2-5x-3=0\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{5+\sqrt{37}}{2}\left(tm\right)\\x=\dfrac{5-\sqrt{37}}{2}\left(tm\right)\end{matrix}\right.\)

Vậy ...

\(3,ĐK:x\ge-1\\ PT\Leftrightarrow3\left(x^2-x+1\right)-2\left(x+1\right)=5\sqrt{x^3+1}\) 

Đặt \(\left\{{}\begin{matrix}\sqrt{x+1}=a\\\sqrt{x^2-x+1}=b\end{matrix}\right.\left(a,b\ge0\right)\)

\(PT\Leftrightarrow3b^2-2a^2=5ab\\ \Leftrightarrow2a^2+5ab-3b^2=0\\ \Leftrightarrow\left[{}\begin{matrix}a=2b\\a=-3b\left(vn\right)\end{matrix}\right.\Leftrightarrow a=2b\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{5+\sqrt{37}}{2}\\x=\dfrac{5-\sqrt{37}}{2}\end{matrix}\right.\left(\text{giống bài 2}\right)\)

Lời giải:

a.

Diện tích mảnh đất là: $12.10=120$ (m²)

Diện tích phần đất trồng hoa: $6.8=48$ (m²)

b.

Diện tích trồng cỏ là: $120-48=72$ (m²)

Tổng tiền công chi trả để trồng hoa và cỏ là:

$48.40 000 +72.30 000=4080000$ (đồng)

Đề bài đâu rồi ạ, có đề mới giải được ạ

ah/chị tham khảo ạ:

Chọn B

Mặt cầu tâm \(I\left(1;1;0\right)\) bán kính \(R=5\)

\(\Rightarrow IA=\sqrt{6^2+8^2}=10=2R\) 

Gọi C là trung điểm IA \(\Rightarrow C\left(4;5;0\right)\Rightarrow IC=R=5\Rightarrow C\in\left(S\right)\)

Gọi D là trung điểm IC \(\Rightarrow D\left(\dfrac{5}{2};3;0\right)\), đồng thời do D là trung điểm IC \(\Rightarrow MD\perp IC\) và IM=IC=R hay tam giác MDF vuông tại D

Lại có: \(CM=CA=CI=R\Rightarrow\) tam giác AMI vuông tại M

\(\Rightarrow\Delta_VMID\sim\Delta_VAIM\) (chung góc I)

\(\Rightarrow\dfrac{MA}{MD}=\dfrac{AI}{AM}=\dfrac{2R}{R}=2\Rightarrow MA=2MD\)

\(\Rightarrow P=MA+2MB=2MD+2MB=2\left(MD+MB\right)\ge2DB=2\sqrt{\left(\dfrac{5}{2}\right)^2+\left(3-8\right)^2+0^2}=5\sqrt{5}\)

B

30.today, to record songs, it takes __________.

A. longer than it used to do

B. shorter than it used to do

C. only one or two days

D. the same amount of time as the 1960s

31.Today’s record procedure results in ________.

A. different sounds of recorded songs and live- performed songs.

B. the mixture between CDs and live concert

C. some special effects on songs

D. differences invoices and instruments played

32. Which of the following is NOT true about the new computer programme?

A. It is predicted to change the music future.

B. It can imitate singers‟ voice.

C. It can sing only one recorded song of the singer.

D. The singer does not necessarily present to really sing.

33.Record companies don’t always ________.

A. suggest the outfits of the band

B. tell the band what to say

C. give the band freedom to do things

D. decide the songs the band will play

34.The word “that” in the passage refers to ________.

A. soap powder

B. an image

C. the band

D. a company