Question

Tìm x ; y biết \(\frac{1+2\times y}{18}=\frac{1+4\times y}{24}=\frac{1+6\times y}{6\times x}\)

Answer 1

Ta có:

\(\frac{1+2y}{18}=\frac{1+4y}{24}=\frac{1+6y}{6x}=\frac{1+6y+1+2y}{18+6x}=\frac{2+8y}{18+6x}\)\(=\frac{2\left(1+4y\right)}{2\left(9+3x\right)}=\frac{1+4y}{9+3x}\Rightarrow9+3x=24\Rightarrow x=5\)

\(\Rightarrow\left(1+6y\right)18=\left(1+2y\right)30\Rightarrow18+108y=30+60y\)

\(\Rightarrow48y=12\Rightarrow y=\frac{12}{48}=\frac{1}{4}\)

Vậy x = 5 và y = \(\frac{1}{4}\)