Question

[❖ミ★𝓣𝓻𝓪𝓷𝓰 (𝓯𝓪𝓷 𝓛𝓝𝓓)★彡『ʈєɑɱ❖๖ۣۜƝƘ☆...]

Ai giúp tui đi, tui tick nè

Answer 1

[ღ ☪áø /『ʈєɑɱ❖๖ۣۜƝƘ☆』ღ]

\(\frac{x}{5}=\frac{y}{7}=\frac{z}{3}=k\) \(\left(k\ne0\right)\)

\(\Rightarrow x=5k;y=7k;z=3k\)

Ta có : x² - y² - z² = 585

\(\Rightarrow\)\(25k^2+49k^2-9k^2=585\)

\(\Rightarrow\)\(65k^2=585\)

\(\Rightarrow k=9\)

\(\Rightarrow\)k = -3 hoặc 3

Với k=3 thì x=5.3=15; y=7.3=21; z=3.3=9

Với k=−3 thì x=5.(−3)=−15; y=7.(−3)=−21; z=3.(−3)=−9

Vậy (x;y;z)=(15;21;9); (−15;−21;−9)

Answer 2

[Nguyễn Huy Tú]

a, \(\frac{x}{5}=\frac{y}{7}=\frac{z}{3}\Rightarrow\frac{x^2}{25}=\frac{y^2}{49}=\frac{z^2}{9}\)

Theo tính chất dãy tỉ số bằng nhau 

\(\frac{x^2}{25}=\frac{y^2}{49}=\frac{z^2}{9}=\frac{x^2+y^2-z^2}{25+49-9}=\frac{585}{65}=9\)

\(\Rightarrow x^2=225\Rightarrow x=\pm15;y^2=441\Rightarrow y=\pm21;z^2=81\Rightarrow z=\pm9\)

b, Ta có : \(x:y:z=3:4:5\Rightarrow\frac{x}{3}=\frac{y}{4}=\frac{z}{5}\Rightarrow\frac{x^2}{9}=\frac{y^2}{16}=\frac{z^2}{25}\)

Theo tính chất dãy tỉ số bằng nhau 

\(\frac{x^2}{9}=\frac{y^2}{16}=\frac{z^2}{25}=\frac{2x^2+2y^2-3z^2}{18+32-75}=-\frac{100}{-25}=4\)

\(\Rightarrow x^2=36\Rightarrow x=\pm6;y^2=64\Rightarrow y=\pm8;z^2=100\Rightarrow z=\pm10\)