Sửa đề : \(\frac{x}{2}=\frac{y}{3};\frac{y}{4}=\frac{z}{5}\)và \(x^2-y^2-z^2=-16\)

Ta có : \(\frac{x}{2}=\frac{y}{3}\Leftrightarrow2y=3x\Rightarrow x=\frac{2y}{3}\left(1\right)\)

            \(\frac{y}{4}=\frac{z}{5}\Leftrightarrow4z=5y\Rightarrow z=\frac{5y}{4}\left(2\right)\)

Thay (1) và (2) vào biểu thức \(x^2-y^2-z^2=-16\);ta được : 

\(\left(\frac{2y}{3}\right)^2-y^2-\left(\frac{5y}{4}\right)^2=-16\)

\(\Leftrightarrow\frac{4y}{9}^2-y^2-\frac{25y^2}{16}=-16\)

\(\Leftrightarrow64y^2-144y^2-225y^2=-16.144\)

\(\Leftrightarrow-305y^2=-2304\)

\(\Leftrightarrow y^2=\frac{2304}{305}\Rightarrow y=\sqrt{\frac{2304}{305}}=2,748472005\)

Với \(y=\sqrt{\frac{2304}{305}}\Rightarrow x=\frac{2.\sqrt{\frac{2304}{305}}}{3}=-183231467;z=\frac{5.\sqrt{\frac{2034}{305}}}{4}=3,435590006\)

Vậy ................. 

hình như câu a sai đề rồi bạn ơi

Uk de mik sưa

Ban giai các cau khac mik voi

a ) x² - 10x 

= x(x - 10)

b) x² + 2x - 3 

= x² - x + 3x - 3

= x(x - 1) + 3(x - 1)

= (x + 3)(x - 1)

c) x² + 4 + 4x) = (x + 2)²

LÀM CHO Ý KHÓ NHẤT NHA

\(x^4+1=x^4-x^3+x^2+x^3-x^2+x+x^2-x+1\)

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

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

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

Câu 1 :

a, 8.( -5 ).( -4 ).2

= [ 8.2 ].[( -5 ).(-4 ]

= 16.20

= 320

b, \(1\frac{3}{7}+\frac{-1}{3}+2\frac{4}{7}\)

\(=\frac{10}{7}+\frac{-1}{3}+\frac{18}{7}\)

\(=\frac{11}{3}\)

c, \(\frac{8}{5}.\frac{2}{3}+\frac{-5.5}{3.5}\)

\(=\frac{8}{3}+\frac{-5}{3}\)

\(=\frac{3}{3}=1\)

d, \(\frac{6}{7}+\frac{5}{8}:5-\frac{3}{16}.\left(-2\right)^2\)

\(=\frac{6}{7}+\frac{1}{8}-\frac{3}{16}.4\)

\(=\frac{55}{56}-\frac{3}{4}\)

\(=\frac{13}{56}\)

Câu 2 :

a, 2x + 10 = 16

    2x = 16 + 10

    2x = 26

    x = 26 : 2

    x = 13

b, \(x-\frac{1}{3}=\frac{5}{4}\)

\(x=\frac{5}{4}+\frac{1}{3}\)

\(x=\frac{19}{12}\)

c, \(2x+3\frac{1}{3}=7\frac{1}{3}\)

\(2x+\frac{10}{3}=\frac{22}{3}\)

\(2x=\frac{22}{3}-\frac{10}{3}\)

\(2x=4\)

\(x=4:2\)

\(x=2\)

d, \(\left(\frac{2}{11}+\frac{1}{3}\right)x=\left(\frac{1}{7}-\frac{1}{8}\right).56\)

\(\frac{17}{33}x=1\)

\(x=1-\frac{17}{33}\)

\(x=\frac{16}{33}\)

1. \(\frac{x-3}{x+2}=\frac{3}{4}\)

=> \(4(x-3)=3(x+2)\)

=> 4x - 12 = 3x + 6

=> 4x - 12 - 3x = 6

=> 4x - 3x - 12 = 6

=> x = 18

2. \(\frac{4-x}{x-1}=\frac{-5}{6}\)

=> 6[4 - x] = -5[x - 1]

=> 24 - 6x = 5 - 5x

=> 24 - 6x - 5 = 5x

=> 24 - 5 = 6x - 5x

=> 19 = x

=> x = 19

3. \(\frac{3-x}{-x+2}=\frac{-1}{3}\)

=> 3[3 - x] = -1[-x + 2]

=> 9 - 3x = x - 2

=> 9 - 3x + x = -2

=> 9 - 4x = -2

=> 4x = 9 - [ -2]

=> 4x = 9 + 2 = 11

=> x = 11/4

4. \(\frac{x-1}{12}=\frac{-3}{1-x}\)

=> [x-1][1-x] = -36

=> -[x-1]² = -36

=> [x-1]² = 36

=> [x-1]² = 6²

=> x -1 = 6 hoặc x - 1 = -6

=> x = 7 hoặc x = -5

5 . |x - 3 | - 8 = -4

=> |x - 3| = -4 + 8

=> |x - 3| = 4

=> x - 3 = 4 hoặc x - 3 = -4

=> x = 7 hoặc x = -1

Mấy bài sau tương tự

b) y/8 + 8y - 56,78 = 69,11 . 2

y/8+ 64y/8 = 138.22+ 56.78

65y/8 =195

65y= 1560

y= 24 

cho mik hỏi câu a đề có đúng ko vậy

câu a mình chép nhầm, thank bn

a/b nhân 4 cộng 1/6 = 17/6 số phải tìm là bao nhiêu

Cậu cho nhiều quá

Mỗi bài mình làm một dạng thôi nhé!

1) \(\left(\frac{3}{2}-\frac{x}{y}\right)+\frac{5}{7}=\frac{11}{14}\)

\(\Rightarrow\frac{x}{y}=\frac{3}{2}-\left(\frac{11}{14}-\frac{5}{7}\right)=\frac{10}{7}\)

2) a) 

\(\frac{17}{9}+\frac{19}{13}+\frac{14}{6}+\frac{7}{13}+\frac{10}{6}+\frac{1}{9}\)

\(=\left(\frac{17}{9}+\frac{1}{9}\right)+\left(\frac{19}{13}+\frac{7}{13}\right)+\left(\frac{14}{6}+\frac{10}{6}\right)\)

\(=2+2+4\)

\(=8\)

3) a) 

\(A=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{42}\)

\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{6.7}\)

\(A=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{6}-\frac{1}{7}\)

\(A=\frac{1}{1}-\frac{1}{7}=\frac{6}{7}\)

4) a)

\(y.\frac{5}{6}=1+\frac{1}{2}\)

\(\Rightarrow y.\frac{5}{6}=\frac{3}{2}\)

\(\Rightarrow y=\frac{3}{2}.\frac{6}{5}=\frac{9}{5}\)