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the sum of reciprocal of two numbers is 7. the larger reciprocal exceeds the smaller one by 7/3 . find the numbers

Sagot :

[tex]\frac{1}{x}=first number[/tex]
[tex]\frac{1}{x}+\frac{7}{3}=second number[/tex]

[tex]\frac{1}{x}+\frac{1}{x}+\frac{7}{3}=7[/tex]
[tex]\frac{2}{x}+\frac{7}{3}=7[/tex]
[tex]\frac{2}{x}=\frac{14}{3}[/tex]
[tex]2=\frac{14x}{3}[/tex]
6=14x
[tex]x=\frac{3}{7}[/tex]

The first number is 3/7 and the second number is 58/21