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have 1/y+1/z=a/x,1/x+1/z=b1/y,1/y+1/x=c1/z .This leads to (a+1)/x=(b+1)/y=(c+1)/z=k, and then to 1/(a+1)+1/(b+1)+1/(c+1)=1.Since x,y,z need to be distinct distinct, so are a,b,c , hence the only solution is 2,3,6. the question was: Find three distinct positive integers with the least possible sum such that the sum of the reciprocals of any two integers among them is an integral multiple of the reciprocal of the third integer. Plse make me understand the solution fast.need it immediately. have 1/y+1/z=a/x,1/x+1/z=b1/y,1/y+1/x=c1/z .This leads to (a+1)/x=(b+1)/y=(c+1)/z=k, and then to 1/(a+1)+1/(b+1)+1/(c+1)=1.Since x,y,z need to be distinct distinct, so are a,b,c , hence the only solution is 2,3,6. the question was: Find three distinct positive integers with the least possible sum such that the sum of the reciprocals of any two integers among them is an integral multiple of the reciprocal of the third integer. Plse make me understand the solution fast.need it immediately.
Dear student, The solutionis quite clear.. 1/y+1/z=a/x,1/x+1/z=b1/y,1/y+1/x=c1/z .This leads to (a+1)/x=(b+1)/y=(c+1)/z=k, and then to 1/(a+1)+1/(b+1)+1/(c+1)=1.Since x,y,z need to be distinct distinct, so are a,b,c , hence the only solution is 2,3,6 Please feel free to ask your queries here. We are all IITians and here to help you in your IIT JEE preparation. All the best. Win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian. Now you score 5+15 POINTS by uploading your Pic and Downloading the Askiitians Toolbar respectively : Click here to download the toolbar.. Askiitians Expert Sagar Singh B.Tech, IIT Delhi
Dear student,
The solutionis quite clear..
1/y+1/z=a/x,1/x+1/z=b1/y,1/y+1/x=c1/z .This leads to (a+1)/x=(b+1)/y=(c+1)/z=k, and then to 1/(a+1)+1/(b+1)+1/(c+1)=1.Since x,y,z need to be distinct distinct, so are a,b,c , hence the only solution is 2,3,6
Please feel free to ask your queries here. We are all IITians and here to help you in your IIT JEE preparation. All the best. Win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian. Now you score 5+15 POINTS by uploading your Pic and Downloading the Askiitians Toolbar respectively : Click here to download the toolbar.. Askiitians Expert Sagar Singh B.Tech, IIT Delhi
Please feel free to ask your queries here. We are all IITians and here to help you in your IIT JEE preparation.
All the best.
Win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian.
Now you score 5+15 POINTS by uploading your Pic and Downloading the Askiitians Toolbar respectively : Click here to download the toolbar..
Askiitians Expert
Sagar Singh
B.Tech, IIT Delhi
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