Tìm x, y, z, t ∈ Z biết:

a, \(\dfrac{5}{x}=\dfrac{-10}{12}\)       b, \(\dfrac{4}{-6}=\dfrac{x+3}{9}\)            c, \(\dfrac{x-1}{25}=\dfrac{4}{x-1}\)    d, \(\dfrac{x+1}{y}=\dfrac{-3}{5}\)

e, \(\dfrac{-12}{6}=\dfrac{x}{5}=\dfrac{-y}{3}=\dfrac{Z}{-17}=\dfrac{-t}{-9}\)

h, \(\dfrac{-24}{-6}=\dfrac{x}{3}=\dfrac{4}{y^2}=\dfrac{Z^3}{-2}\)

tìm x :

a) \(\dfrac{x+1}{7}+\dfrac{x+1}{8}=\dfrac{x+1}{9}+\dfrac{x+1}{10}\)

b) \(\dfrac{x+1}{12}+\dfrac{x^2}{11}=\dfrac{x+3}{10}+\dfrac{x+4}{9}\)

c) \(\dfrac{x-2}{x-1}=\dfrac{x+4}{x+7}\)

d)\(\dfrac{3x+2}{5x+7}=\dfrac{3x-1}{5x-3}\)

2 tìm x,y,z

a) \(\dfrac{x}{2}=\dfrac{y}{3},\dfrac{y}{4}=\dfrac{z}{5}vàx^2-y^2=-16\)

b)2x=3y,5x=7z và 3x-7y+5z=30

Tìm x,y,z trong dãy tỉ số bằng nhau

1)\(\dfrac{3x}{8}=\dfrac{3y}{64}=\dfrac{3z}{216}\)và \(2x^2+2y^2.z^2=1\)

2) \(\dfrac{2x+1}{5}=\dfrac{4y-5}{9}=\dfrac{2x+4y-4}{7x}\)

3) \(\dfrac{x^3+y^3}{6}=\dfrac{x^3-2y^3}{4}\)và x⁶ . y⁶ =14

4) \(\dfrac{x+4}{6}=\dfrac{3y-1}{8}=\dfrac{3y-x-5}{x}\)

5) \(\dfrac{3}{x-1}=\dfrac{4}{y-2}=\dfrac{5}{z-3}\)và x.y.z=192

6)\(\dfrac{x-y}{3}=\dfrac{x+y}{13}=\dfrac{x.y}{200}\)

7)\(\dfrac{x+1}{2}=\dfrac{y-1}{3}=\dfrac{z+2}{4}=\dfrac{x+y+z+2}{2x+5}\)

8) \(\dfrac{15}{x-9}=\dfrac{20}{y-12}=\dfrac{40}{z-24}\)và x.y = 1200

9)\(\dfrac{40}{x-30}=\dfrac{20}{y-15}=\dfrac{28}{z-21}\) và x.y.z = 22400

10)15x = -10y =6z và x.y.z = -30000

11) Cho\(\dfrac{x+1}{3}=\dfrac{y-2}{5}=\dfrac{2z+14}{9}\)và x+z=y

12) Cho \(\dfrac{x}{3}=\dfrac{y}{4}\)và \(\dfrac{y}{5}=\dfrac{z}{6}\).Tính M=\(\dfrac{2x+3y+4z}{3x+4y+5z}\)

Câu 1 The function mm is defined on the real numbers by m(k) = \dfrac{k+2}{k+8}m(k)= k+8 k+2 ​ . What is the value of 10\times m(2)10×m(2)? Answer: Câu 2 The function ff is defined on the real numbers by f(x)= ax-3f(x)=ax−3. What is the value of a if f(3)=9f(3)=9? Answer: Câu 3 The function ff is defined on the real numbers by f(x)= 2x+a-3f(x)=2x+a−3. What is the value of a if f(-5)=11f(−5)=11? Answer: Câu 4 The function ff is defined on the real numbers by f(x) = 2 + x-x^2f(x)=2+x−x 2 . What is the value of f(-3)f(−3)? Answer: Câu 5 Given a real number aa and a function ff is defined on the real numbers by f(x)=-6\times|3x|-4f(x)=−6×∣3x∣−4. Compare: f(a)f(a) f(-a)f(−a) Câu 6 There are ordered pairs (x;y)(x;y) where xx and yy are integers such that \dfrac{5}{x}+\dfrac{y}{4}=\dfrac{1}{8} x 5 ​ + 4 y ​ = 8 1 ​ Câu 7 Given a negative number kk and a function ff is defined on the real numbers by f(x)=\dfrac{6}{13}xf(x)= 13 6 ​ x. Compare: f(k)f(k) f(-k)f(−k) Câu 8 Given a positive number kk and a function ff is defined on the real numbers by f(x)=\dfrac{-3}{4}x+4f(x)= 4 −3 ​ x+4. Compare: f(k)f(k) f(-k)f(−k). Câu 9 A=(1+2+3+\ldots+90) \times(12 \times34-6 \times 68):(\dfrac{1}{3}+\dfrac{1}{4}+\dfrac{1}{5}+\dfrac{1}{6})=A=(1+2+3+…+90)×(12×34−6×68):( 3 1 ​ + 4 1 ​ + 5 1 ​ + 6 1 ​ )= Câu 10 Given that \dfrac{2x+y+z+t}{x}=\dfrac{x+2y+z+t}{y}=\dfrac{x+y+2z+t}{z}=\dfrac{x+y+z+2t}{t} x 2x+y+z+t ​ = y x+2y+z+t ​ = z x+y+2z+t ​ = t x+y+z+2t ​ . The negative value of \dfrac{x+y}{z+t}+\dfrac{y+z}{t+x}+\dfrac{z+t}{x+y}+\dfrac{t+x}{y+z} z+t x+y ​ + t+x y+z ​ + x+y z+t ​ + y+z t+x ​ is

Tìm x,y,z biết:

a, x : y : z = 10 : 3 : 4 và x + 2y - 3z = -20

b, \(\dfrac{x}{2}\) = \(\dfrac{y}{3}\)  và \(\dfrac{y}{5}\) = \(\dfrac{z}{4}\) và x - y + z = -49

c, \(\dfrac{x}{2}\)= \(\dfrac{y}{3}\) =\(\dfrac{z}{4}\) và xy + \(z^2\)= 88

d, \(\dfrac{x}{5}\)= \(\dfrac{y}{7}\) = \(\dfrac{z}{3}\) và \(x^2\) + \(y^2\) + \(z^2\) = 415

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