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Suppose m, n are positive integers such...

Suppose m, n are positive integers such that `6^(m) + 2^(m+n) 3^(m) + 2^(n) = 332`. The value of the expression `m^(2) + nm + n^(2)` is -

A

`7`

B

`13`

C

`19`

D

`21`

Text Solution

Verified by Experts

The correct Answer is:
C
`6^(m) + 2^(m+n) 3^(w) + 2^(n) = 332`
maximum possible value of m is 3
checking for `m = 3,2` and .1
we get `m = 2, n = 3, w = 2`
`m^(2) + mn + n^(2) = 4 + 6 + 9 = 19`
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