Question

a) x:y:z= 2:3:5 & xyz=810

b)\(\dfrac{x^3}{8}\) =\(\dfrac{y^3}{27}\)=\(\dfrac{z^3}{64}\)& x²+2y²-3z²= -650

Answer 1

a) Ta có: x : y : z = 2 : 3 : 5

⇒ \(\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{5}\)

Giả sử: \(\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{5}=k\)

⇒ x = 2k ; y = 3k ; z = 5k

Ta có: xyz = 810

⇒ 2k . 3k . 5k = 810

30 . k³ = 810

k³ = 810 : 30

k³ = 27

⇒ k = 3

⇒ k = 3 ⇒ x = 2 . 3 = 6

y = 3 . 3 = 9

z = 5 . 3 = 15

Vậy x = 6 ; y = 9 ; z = 15

b) Ta có: \(\dfrac{x^3}{8}=\dfrac{y^3}{27}=\dfrac{z^3}{64}\)

⇒ \(\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{4}\) ⇒ \(\dfrac{x^2}{4}=\dfrac{2y^2}{18}=\dfrac{3z^2}{48}\)

Áp dụng tính chất dãy tỉ số bằng nhau ta có

\(\dfrac{x^2}{4}=\dfrac{2y^2}{18}=\dfrac{3z^2}{48}=\dfrac{x^2+2y^2-3z^2}{4+18-48}\)

\(=\dfrac{-650}{-26}=25\)

+) \(\dfrac{x}{2}=25\) ⇒ x = 50

\(\dfrac{y}{3}=25\) ⇒ y = 75

\(\dfrac{z}{4}=25\) ⇒ z = 100

Vậy x = 50 ; y = 75 ; z = 100