Ta có: \(\frac{x}{2}=\frac{y}{3}\) và\(\frac{y}{5}=\frac{z}{6}\)và \(2x-y+z=46\)

\(\Rightarrow\frac{x}{10}=\frac{y}{15}=\frac{z}{18}\)và \(2x-y+z=46\)

\(\Rightarrow\frac{2x}{20}=\frac{y}{15}=\frac{z}{18}\)và\(2x-y+z=46\)

Áp dụng tính chất của dãy tỉ số bằng nhau, ta có:

\(\frac{2x}{20}=\frac{y}{15}=\frac{z}{18}=\frac{2x-y+z}{20-15+18}=\frac{46}{23}=2\)

Ta có: \(\frac{x}{10}=\frac{2x}{20}=2\Rightarrow x=2.10=20\)

          \(\frac{y}{15}=2\Rightarrow y=2.15=30\)

          \(\frac{z}{18}=2\Rightarrow z=2.18=36\)

Vậy:\(x=20;y=30\)và\(z=36\)

Bài1:

a. Đây là dãy số cách đều 3 đơn vị.

Có số số hạng là: ( 299 - 2) : 3 + 1 = 100 (số hạng)

Tổng của dãy số là : (299+1) x 100 : 2 = 15000

b. Đây là dãy số cách đều 5 đơn vị.

Có số số hạng là : (51 - 1) : 5 +1 = 11 ( Số hạng)

Tổng: ( 51 + 1) x 11 : 2 = 286

Bài 2:

(2x-15)^5 = (2x-15)^3

(2x-15)^2 = 1

(2x-15)^2 = 1^2

=> 2x-15 = 1

2x = 16

x = 8

a) \(\left(2x-1\right)+\frac{3}{15}=\frac{3}{2}\)

\(\Rightarrow2x-1=\frac{3}{2}-\frac{3}{15}=\frac{13}{10}\)

\(\Rightarrow2x=\frac{13}{10}+1=\frac{23}{10}\)

\(\Rightarrow x=\frac{23}{20}\)

b) \(x+\frac{46}{15}=1,5\)

\(\Rightarrow x+\frac{46}{15}=\frac{3}{2}\)

\(\Rightarrow x=\frac{3}{2}-\frac{46}{15}\)

\(\Rightarrow x=\frac{-47}{30}\)

c) \(\left(-2x+1\right)+\frac{3}{15}=\frac{5}{3}\)

\(\Rightarrow-2x+1=\frac{5}{3}-\frac{3}{15}=\frac{22}{15}\)

\(\Rightarrow-2x=\frac{7}{15}\Rightarrow x=\frac{-7}{30}\)

câu 1:

= \(-102+\left[9.\left(-2\right)+8\right]:13\)

= \(-102-\frac{10}{13}\)

= \(\frac{-1336}{13}\)

Câu 2

a)

=\(-15\left(53+47\right)\)

= -15.100

=-1500

b)

= -46 ( 214+27-41)

= -46.200

= -9200

Giải:

a) \(\dfrac{-5}{8}=\dfrac{x}{16}\) 

\(\Rightarrow x=\dfrac{16.-5}{8}=-10\) 

\(\dfrac{3x}{9}=\dfrac{2}{6}\) 

\(\Rightarrow3x=\dfrac{2.9}{6}=3\) 

\(\Rightarrow x=1\)

b) \(\dfrac{x+3}{15}=\dfrac{1}{3}\)  

\(\Rightarrow x+3=\dfrac{1.15}{3}=5\) 

\(\Rightarrow x=2\)

\(\dfrac{6}{2x+1}=\dfrac{2}{7}\) 

\(\Rightarrow2x+1=\dfrac{6.7}{2}=21\) 

\(\Rightarrow x=10\)

c) \(\dfrac{4}{x-6}=\dfrac{y}{24}=\dfrac{-12}{18}\) 

\(\Rightarrow\dfrac{4}{x-6}=\dfrac{-12}{18}\) 

\(\Rightarrow x-6=\dfrac{18.4}{-12}=-6\) 

\(\Rightarrow x=0\) 

\(\Rightarrow\dfrac{y}{24}=\dfrac{-12}{18}\) 

\(\Rightarrow y=\dfrac{-12.24}{18}=-16\) 

 \(\dfrac{3-x}{-12}=\dfrac{16}{y+1}=\dfrac{192}{-72}\) 

\(\Rightarrow\dfrac{3-x}{-12}=\dfrac{192}{-72}\) 

\(\Rightarrow3-x=\dfrac{192.-12}{-72}=32\) 

\(\Rightarrow x=-29\) 

\(\Rightarrow\dfrac{16}{y+1}=\dfrac{192}{-72}\) 

\(\Rightarrow y+1=\dfrac{16.-72}{192}=-6\) 

d) \(\dfrac{-2}{3}< \dfrac{x}{5}< \dfrac{-1}{6}\) 

\(\Rightarrow\dfrac{-20}{30}< \dfrac{6x}{30}< \dfrac{-5}{30}\) 

\(\Rightarrow6x\in\left\{-18;-12;-6\right\}\) 

\(\Rightarrow x\in\left\{-3;-2;-1\right\}\) 

\(\dfrac{-1}{5}\le\dfrac{x}{8}\le\dfrac{1}{4}\) 

\(\Rightarrow\dfrac{-8}{40}\le\dfrac{5x}{40}\le\dfrac{10}{40}\) 

\(\Rightarrow5x\in\left\{-5;0;5;10\right\}\) 

\(\Rightarrow x\in\left\{-1;0;1;2\right\}\) 

e) \(\dfrac{x+46}{20}=x\dfrac{2}{5}\) 

\(\Rightarrow\dfrac{x+46}{20}=x+\dfrac{2}{5}\) 

\(\Rightarrow\dfrac{x+46}{20}=\dfrac{5x+2}{5}\) 

\(\Rightarrow5.\left(x+46\right)=20.\left(5x+2\right)\) 

\(\Rightarrow5x+230=100x+40\) 

\(\Rightarrow5x-100x=40-230\) 

\(\Rightarrow-95x=-190\) 

\(\Rightarrow x=-190:-95\) 

\(\Rightarrow x=2\) 

\(y\dfrac{5}{y}=\dfrac{86}{y}\) 

\(\Rightarrow y+\dfrac{5}{y}=\dfrac{86}{y}\) 

\(\Rightarrow\dfrac{y^2+5}{y}=\dfrac{86}{y}\) 

\(\Rightarrow y^2+5=86\) 

\(\Rightarrow y^2=86-5\) 

\(\Rightarrow y^2=81\) 

\(\Rightarrow\left[{}\begin{matrix}y=9\\y=-9\end{matrix}\right.\) 

Chúc bạn học tốt!

7,x²-2xy+y²+3x-3y=(x-y)²+3(x-y)=(x-y)(x-y+3)

8,x⁴+4=(x⁴+4x²+4)-4x²=(x²+2)²-(2x)²=(x²-2x+2)(x²+2x+2)

9,4x(x+1)²-5x²(x+1)-4.(x+1)=(x+1)\(\left[4x\left(x+1\right)-5x^2-4\right]\)=(x+1)(4x²+4x-5x²-4)=(x+1)(-x²+4x-4)=-(x+1)(x-2)²

7: \(x^2-2xy+y^2+3x-3y\)

\(=\left(x-y\right)^2+3\cdot\left(x-y\right)\)

\(=\left(x-y\right)\left(x-y+3\right)\)

8: \(x^4+4\)

\(=x^4+4x^2+4-4x^2\)

\(=\left(x^2+2\right)^2-4x^2\)

\(=\left(x^2-2x+2\right)\left(x^2+2x+2\right)\)

9: \(4x\left(x+1\right)^2-5x^2\left(x+1\right)-4\left(x+1\right)\)

\(=\left(x+1\right)\left(4x^2+4x-5x^2-4\right)\)

\(=\left(x+1\right)\left(-x^2+4x-4\right)\)

\(=-\left(x+1\right)\left(x-2\right)^2\)

10: \(\left(1+2x\right)\left(1-2x\right)-\left(x+2\right)\left(x-2\right)\)

\(=1-4x^2-x^2+4\)

\(=-5x^2+5\)

\(=-5\left(x-1\right)\left(x+1\right)\)

1) Ta có: \(\dfrac{a-6\sqrt{a}+9}{5\sqrt{a}-15}\)

\(=\dfrac{\left(\sqrt{a}-3\right)^2}{5\left(\sqrt{a}-3\right)}\)

\(=\dfrac{\sqrt{a}-3}{5}\)

2) Ta có: \(5x-\sqrt{x^2-10x+25}\)

\(=5x-\left|x-5\right|\)

\(=5x-5+x\)

=6x-5

3) Ta có: \(\dfrac{\sqrt{x^2-2x+1}}{x-1}\)

\(=\dfrac{\left|x-1\right|}{\left(x-1\right)\left(x+1\right)}\)

\(=\dfrac{\pm1}{x+1}\)

4) Ta có: \(3\sqrt{5}-\sqrt{46-6\sqrt{5}}\)

\(=3\sqrt{5}-3\sqrt{5}+1\)

=1