Question

Tìm x

\(\dfrac{10+x}{17+x}=\dfrac{10.11+50.55+70.77}{11.12+55.60+77.84}\left(x\ne-17\right)\)

Answer 1

\(\dfrac{10+x}{17+x}=\dfrac{10\cdot11+50\cdot55+70\cdot77}{11\cdot12+55\cdot66+77\cdot84}\)

\(\Leftrightarrow\dfrac{10+x}{17+x}=\dfrac{10\cdot11+5\cdot10\cdot111+7\cdot10\cdot11}{11\cdot12+5\cdot11\cdot12+7\cdot11\cdot12}\)

\(\Leftrightarrow\dfrac{10+x}{17+x}=\dfrac{10\cdot11\left(1+5+7\right)}{11\cdot12\left(1+5+7\right)}\)

\(\Leftrightarrow\dfrac{10+x}{17+x}=\dfrac{5}{6}\)

\(\Leftrightarrow6\left(10+x\right)=5\left(17+x\right)\)

\(\Leftrightarrow60+6x=85+5x\)

\(\Leftrightarrow6x-5x=85-60\)

\(\Leftrightarrow x=25\) (TM x\(\ne17\))

Vậy ...................................