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Question Number 166943 by cortano1 last updated on 03/Mar/22

Commented by blackmamba last updated on 03/Mar/22

 By Ladder theorem   (1/(x+4+5+10))+(1/(10))=(1/(4+10))+(1/(5+10))  ⇒(1/(x+19))=(1/(14))+(1/(15))−(1/(10))  ⇒(1/(x+19))=(4/(105)) ; x=((29)/4)=7.25

$$\:{By}\:{Ladder}\:{theorem} \\ $$$$\:\frac{\mathrm{1}}{{x}+\mathrm{4}+\mathrm{5}+\mathrm{10}}+\frac{\mathrm{1}}{\mathrm{10}}=\frac{\mathrm{1}}{\mathrm{4}+\mathrm{10}}+\frac{\mathrm{1}}{\mathrm{5}+\mathrm{10}} \\ $$$$\Rightarrow\frac{\mathrm{1}}{{x}+\mathrm{19}}=\frac{\mathrm{1}}{\mathrm{14}}+\frac{\mathrm{1}}{\mathrm{15}}−\frac{\mathrm{1}}{\mathrm{10}} \\ $$$$\Rightarrow\frac{\mathrm{1}}{{x}+\mathrm{19}}=\frac{\mathrm{4}}{\mathrm{105}}\:;\:{x}=\frac{\mathrm{29}}{\mathrm{4}}=\mathrm{7}.\mathrm{25}\: \\ $$

Commented by Tawa11 last updated on 03/Mar/22

Great sir

$$\mathrm{Great}\:\mathrm{sir} \\ $$

Answered by mr W last updated on 03/Mar/22

(x_1 /4)=((x+5)/(4+10)) ⇒x_1 =((4(x+5))/(4+10))  (x_2 /5)=((x+4)/(5+10)) ⇒x_2 =((5(x+4))/(5+10))  x_1 +x_2 =x=((4(x+5))/(4+10))+((5(x+4))/(5+10))  ⇒x=((29)/4)=7.25

$$\frac{{x}_{\mathrm{1}} }{\mathrm{4}}=\frac{{x}+\mathrm{5}}{\mathrm{4}+\mathrm{10}}\:\Rightarrow{x}_{\mathrm{1}} =\frac{\mathrm{4}\left({x}+\mathrm{5}\right)}{\mathrm{4}+\mathrm{10}} \\ $$$$\frac{{x}_{\mathrm{2}} }{\mathrm{5}}=\frac{{x}+\mathrm{4}}{\mathrm{5}+\mathrm{10}}\:\Rightarrow{x}_{\mathrm{2}} =\frac{\mathrm{5}\left({x}+\mathrm{4}\right)}{\mathrm{5}+\mathrm{10}} \\ $$$${x}_{\mathrm{1}} +{x}_{\mathrm{2}} ={x}=\frac{\mathrm{4}\left({x}+\mathrm{5}\right)}{\mathrm{4}+\mathrm{10}}+\frac{\mathrm{5}\left({x}+\mathrm{4}\right)}{\mathrm{5}+\mathrm{10}} \\ $$$$\Rightarrow{x}=\frac{\mathrm{29}}{\mathrm{4}}=\mathrm{7}.\mathrm{25} \\ $$

Commented by Tawa11 last updated on 03/Mar/22

Great sir

$$\mathrm{Great}\:\mathrm{sir} \\ $$

Commented by Ari last updated on 03/Mar/22

Where are you based on creating reports sir

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