Question

cho hai số x;y(0>x>y).Biết \(\frac{x}{3}=\frac{y}{2}\) và 6xy=1.tìm x

Answer 1

đặt x/3=y/2=k

=>x=3k;y=2k

6xy=1 =>xy=1/6

=>xy=3k.2k =6.k^2=1/6

=>k^2=1/6:6=1/36=(+1/6)^2

=>k=+1/6

+)k=1/6=>x=1/2=0,5;y=1/3

+)k=-1/6=>x=-1/2=-0,5;y=-1/3

ta có:0.x>y=>x;y là số âm

=>x=-1/2;y=-1/3

 

Answer 2

\(\frac{x}{3}=\frac{y}{2}=>\frac{x}{3}.\frac{6y}{12}=\frac{y}{2}.\frac{6y}{12}=>\frac{6xy}{36}=\frac{6.y^2}{24}=\frac{1}{36}\)

=>\(6.y^2=\frac{1}{36}.24=\frac{2}{3}=>y^2=\frac{2}{3}:6=\frac{1}{9}=>y=\frac{1}{3},-\frac{1}{3}\)

Với\(y=\frac{1}{3}=>6x=1:\frac{1}{3}=3=>x=3:6=\frac{1}{2}\)

Với\(y=-\frac{1}{3}=>6x=1:\left(-\frac{1}{3}\right)=-3=>x=-3:6=-\frac{1}{2}\)

Vậy \(x=\frac{1}{2},y=\frac{1}{3}\)

 \(x=-\frac{1}{2},y=-\frac{1}{3}\)