Question

tìm x ,y , z biết

x:y:z =3:4:5 và \(5z^2-3z^2-2y^2=594\)

Answer 1

Từ \(x:y:z=3:4:5\Rightarrow\dfrac{x}{3}=\dfrac{y}{4}=\dfrac{z}{5}\)

\(\Rightarrow\dfrac{3x^2}{27}=\dfrac{2y^2}{32}=\dfrac{5z^2}{125}\)

Theo t/c dãy số bằng nhau :

\(\dfrac{3x^2}{27}=\dfrac{2y^2}{32}=\dfrac{5z^2}{125}=\dfrac{5z^2-2y^2-3x^2}{125-32-27}=\dfrac{594}{66}=9\)

\(\Rightarrow3x^2=9\cdot27=243\Rightarrow x^2=\dfrac{243}{3}=81\Rightarrow x\in\left\{9;-9\right\}\)

\(\Rightarrow2y^2=9\cdot32=288\Rightarrow y^2=\dfrac{288}{2}=144\Rightarrow y\in\left\{12;-12\right\}\)

\(\Rightarrow5z^2=9\cdot125=1125\Rightarrow z^2=\dfrac{1125}{5}=225\Rightarrow z\in\left\{15;-15\right\}\)