Question

Cho hai số \(x,y\left(0>x>y\right)\). Biết \(\frac{x}{3}=\frac{y}{5}\)và  \(x^2\times y^2=225\)
Khi đó \(x=\)___________ , \(y=\)_____________
Giúp mình nha^^

Answer 1

\(\frac{x}{3}=\frac{y}{5}\)

=> \(\frac{x^4}{3^4}=\frac{y^4}{5^4}=\frac{x^2.y^2}{3^2.5^2}=\frac{225}{225}=1\)

=> x⁴ = 3⁴ => x = 3 hoặc x = -3

y⁴ = 5⁴ => x = 5 hoặc x = -5

KL: (x; y) = (3; 5) ; (-3; -5)

Answer 2

Đặt:

\(\frac{x}{3}=\frac{y}{5}=k\)

Ta có:

\(\frac{x}{3}=k\Rightarrow x=k.3\)

\(\frac{y}{5}=k\Rightarrow y=k.5\)

Thế vào \(x^2y^2=225\), ta có:

\(\left(k.3\right)^2.\left(k.5\right)^2=225\)

\(\Rightarrow\left(k^2.15\right)^2=225\)

\(\Rightarrow\left(k^2.15\right)=15\)

\(\Rightarrow k^2=1\)

\(\Rightarrow k=1\)hoặc \(-1\)

x ; y tự tìm bạn.

=> x = -3

y = -5

Answer 3

\(\frac{x}{3}\)=\(\frac{y}{5}\)=> x= \(\frac{3y}{5}\)

mà x² *y²=225

\(\frac{9y^2}{25}\)* y²=225

\(\frac{9y^4}{25}\)=225

\(y^4\)=625

y=5

=>x=3