Question

If 1/a+1/b=1/c and ab=c the what is the average of a and b?

Answer 1

If by average u mean arithmetic mean then it'd be 1/2

Answer 2

Please elaborate the method you used

Answer 3

Explanation:
\[\frac{ 1 }{ a }+\frac{ 1 }{ b }= \frac{ 1 }{ c }\]
this means,
\[\frac{ a+b }{ a*b }=\frac{ 1 }{ c }\]
this implies
\[ac+bc=ab\]
substituting this value of ab in the second equation, ab = c, we get,
\[a ^{2}b+ab ^{2}=ab\]
dividing this entire equation by ab, we get,
\[a+b=1\]
this is the sum of a and b, the average should be sum of the values / no. of values, therefore, the average is
\[\frac{ Sum of values }{ no. of values }=\frac{ a+b }{ 2 }=\frac{ 1 }{ 2 }\]

Answer 4

Thank you! Best Explanation

Answer 5

You are welcome!

Answer 6

hi mruna_cp,

could you please explain how you got \[a ^{2}b + ab ^{2}=ab\]?

Thank you so much