Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\dfrac{x^2}{9}=\dfrac{y^2}{16}=\dfrac{x^2+y^2}{9+16}=\dfrac{100}{25}=4\)
\(\Rightarrow x^2=4.9=36\Rightarrow x=\sqrt{36}=6\\ y^2=4.16=64\Rightarrow y=\sqrt{64}=8\)
Tìm x,y
\(\dfrac{x^2}{9}=\dfrac{y^2}{16},x^2+y^2=100\)
\(\dfrac{x-1}{2}=\dfrac{y-2}{3}=\dfrac{z-3}{4}vax-2y+3z=14\)
\(\dfrac{x}{5}=\dfrac{y}{4}=\dfrac{z}{2}vax^3-y^3=z^3\)
\(\dfrac{x}{3}=\dfrac{y}{4}=\dfrac{z}{2};x^2+y^2=100\)
\(\dfrac{x}{7}=\dfrac{y}{4}=\dfrac{z}{2};x-3x=9\)
\(\dfrac{x}{9}=\dfrac{y}{15}\) và \(x^2-y^2=-16\) Tìm x,y biết:
Tĩm,y,z biết:
a)\(\dfrac{12x-15y}{7}\)=\(\dfrac{20z-12x}{9}\)=\(\dfrac{15y-20z}{11}\)và x+y+z=48
b)\(\dfrac{x+16}{9}\)=\(\dfrac{y-25}{16}\)=\(\dfrac{z+9}{25}\) và \(^{2x^3}\)-1=15
c)\(\dfrac{x}{y+2+1}\)=\(\dfrac{y}{z+x+1}\)=\(\dfrac{z}{x+y-2}\)=x+y+z
d)\(\dfrac{3}{5}\)x=\(\dfrac{2}{3}\)y và \(^{x^2}\)-\(^{y^2}\)= 38
e)\(\dfrac{y+2+1}{x}\)=\(\dfrac{z+x+2}{y}\)=\(\dfrac{x+y+3}{z}\)=\(\dfrac{1}{x+y+z}\)
f)\(\dfrac{1+2y}{18}\)=\(\dfrac{1+4y}{24}\)=\(\dfrac{1+6y}{6x}\)
Tìm các số x,y,z biết:
a)\(\dfrac{x}{y}=\dfrac{7}{20};\dfrac{y}{z}=\dfrac{5}{8}\)và 2x+5y-2x=100
b)5x=8y=20z và x-y-z=3
c)\(\dfrac{6}{11}x=\dfrac{9}{2}y=\dfrac{18}{5}z\)và -x+y+z=-120
Tìm x, y:
\(\dfrac{x}{3}=\dfrac{y}{4}\) và \(x^2-y^2=16\)
Tìm x,y,z, biết :
\(\dfrac{x}{2}=\dfrac{y}{5}=\dfrac{z}{7}\) và x - y + z = 16
