Question

Tìm x, y biết

1.\(\frac{x}{3}=\frac{y}{4}\)và \(x^2+y^2=100\)

2. \(\frac{x}{4}=\frac{y}{3}\)và x.y=12

Answer 1

x/3 = y/4 = k

Nên x = 3k ; y = 4k

(3k)² + (4k)² = 100

=> 9k² + 16k² = 100

=> 25k² = 100

k² = 4

k thuộc {-2;2}

Nếu k = -2 thì x = -6 ; y = -8

Nếu k = 2 thì x = 6 ; y = 8

Answer 2

1. \(\frac{x}{3}=\frac{y}{4}\Rightarrow\frac{x^2}{9}=\frac{y^2}{16}=\frac{x^2+y^2}{9+16}=\frac{100}{25}=4\)

=> \(\frac{x^2}{9}=4\Rightarrow x^2=4.9=36\Rightarrow x=6\text{ hoặc }x=-6\)

=> \(\frac{y^2}{16}=4\Rightarrow y^2=4.16=64\Rightarrow y=8\text{ hoặc }y=-8\)

2. đặt  y/3=x/4=k

=> y=3k; x=4k

x.y=48

=> 3k.4k=48

=> 12k²=48

=> k²=48:12

=> k²=4

=> k=2 hoặc k=-2

TH1: k=2

=> x=4k=4.2=8

=> y=3k=3.2=6

TH2: k=-2

=> x=4k=4.(-2)=-8

=> y=3k=3.(-2)=-6