The product of two numbers is 91 and their arithmetic mean is 10 then the two numbers are

Correct option is (B) 13, 7

Let the numbers are a & b.

\(\therefore\) Their product = ab

And their arithmetic mean \(=\frac{a+b}2\)

\(\therefore ab=91\)        _____________(1)

& \(\frac{a+b}2=10\)                        (Given)

\(\Rightarrow a+b=20\)   _____________(2)

Now, \((a-b)^2=(a+b)^2-4ab\)

\(=20^2-4\times91\)     (From (1) & (2))

\(=400-364\)

\(=36=6^2\)

\(\therefore a-b=6\)   _____________(3)

By adding (2) & (3), we get

\((a+b)+(a-b)=20+6\)

\(\Rightarrow2a=26\)

\(\Rightarrow a=\frac{26}2=13\)

\(\therefore b=20-a\)

\(=20-13=7\)           (From (2))

Hence, both numbers are 13 & 7.

Correct option is B) 13, 7