Question Number 207247 by hardmath last updated on 10/May/24
$$\mathrm{8}\:\:+\:\:\frac{\mathrm{18}}{\mathrm{2}\:\:+\:\:\frac{\mathrm{7}}{\mathrm{5}\:\:+\:\:\frac{\mathrm{2}}{\boldsymbol{\mathrm{x}}}}}\:\:\:=\:\:\:\mathrm{14}\:\:\:\:\:\mathrm{find}:\:\:\:\boldsymbol{\mathrm{x}}\:=\:? \\ $$
Commented by Frix last updated on 10/May/24
$${x}=\mathrm{1} \\ $$
Answered by Rasheed.Sindhi last updated on 11/May/24
$$\mathrm{8}\:\:+\:\:\frac{\mathrm{18}}{\mathrm{2}\:\:+\:\:\frac{\mathrm{7}}{\mathrm{5}\:\:+\:\:\frac{\mathrm{2}}{\boldsymbol{\mathrm{x}}}}}\:\:\:=\:\:\:\mathrm{14}\:\:\:\:\:\mathrm{find}:\:\:\:\boldsymbol{\mathrm{x}}\:=\:? \\ $$$$\Rightarrow\:\:\frac{\mathrm{18}}{\mathrm{2}\:\:+\:\:\frac{\mathrm{7}}{\mathrm{5}\:\:+\:\:\frac{\mathrm{2}}{\boldsymbol{\mathrm{x}}}}}\:\:\:=\:\:\:\mathrm{6}\:\:\: \\ $$$$\Rightarrow\:\:\frac{\mathrm{3}}{\mathrm{2}\:\:+\:\:\frac{\mathrm{7}}{\:\:\frac{\mathrm{5}{x}+\mathrm{2}}{\boldsymbol{\mathrm{x}}}}}\:\:\:=\:\:\:\mathrm{1}\:\:\:\: \\ $$$$\Rightarrow\:\:\frac{\mathrm{3}}{\mathrm{2}\:\:+\:\:\frac{\mathrm{7}{x}}{\:\:\mathrm{5}{x}+\mathrm{2}}}\:\:\:=\:\:\:\mathrm{1}\:\:\:\: \\ $$$$\Rightarrow\frac{\mathrm{3}}{\frac{\mathrm{10}{x}+\mathrm{4}+\mathrm{7}{x}}{\mathrm{5}{x}+\mathrm{2}}}=\mathrm{1} \\ $$$$\Rightarrow\frac{\mathrm{3}\left(\mathrm{5}{x}+\mathrm{2}\right)}{\mathrm{17}{x}+\mathrm{4}}=\mathrm{1} \\ $$$$\Rightarrow\mathrm{15}{x}+\mathrm{6}=\mathrm{17}{x}+\mathrm{4} \\ $$$$\Rightarrow\mathrm{2}{x}=\mathrm{2}\Rightarrow{x}=\mathrm{1} \\ $$