Question

Biết x₁+x₂+x₃+x₄=36 và 4x₁=6x₂=10x₃=12x₄

Tìm x_1,x_2,x₃,x₄

Chán quá~~~bài dễ "xõa" tí đi :)

Answer 1

\(4x_1=6x_2=10x_3=12x_4\Leftrightarrow2x_1=3x_2=5x_3=6x_4\Leftrightarrow\frac{x_1}{\frac{1}{2}}=\frac{x_2}{\frac{1}{3}}=\frac{x_3}{\frac{1}{5}}=\frac{x_4}{\frac{1}{6}}=P\)Thay vào \(x_1+x_2+x_3+x_4=36\Leftrightarrow\frac{1}{2}P+\frac{1}{3}P+\frac{1}{5}P+\frac{1}{6}P=36\)\(\Leftrightarrow\frac{6}{5}P=36\Leftrightarrow P=30\)Vậy, \(x_1=\frac{1}{2}P=15;x_2=\frac{1}{3}P=10;x_3=\frac{1}{5}P=6;x_4=\frac{1}{6}P=5\)

Answer 2

4x₁ = 6x₂ = 10x₃ = 12x₄ => \(\frac{x_1}{\frac{1}{4}}=\frac{x_2}{\frac{1}{6}}=\frac{x_3}{\frac{1}{10}}=\frac{x_4}{\frac{1}{12}}=\frac{x_1+x_2+x_3+x_4}{\frac{1}{4}+\frac{1}{6}+\frac{1}{10}+\frac{1}{12}}=\frac{36}{\frac{36}{60}}=60\)

=> (x₁ ; x₂ ; x₃ ; x₄) = ( \(\frac{60}{4};\frac{60}{6};\frac{60}{10};\frac{60}{12}\)) = ( 15 ; 10 ; 6 ; 5 )