Question

If a + b = 10 what is the value of 2(a + b) + a + b/6 + (a + b) ^ 2 - 2

Answer 1

`(359)/(3)` or
`119~(2)/(3)`

Explanation:

Let
`x=a+b`. Then, the expression just reduces to
`2x+(x)/(6)+x^2-2`.

But we know that
`a+b=x=10`!

Plugging in for
`x` gives
`2(10)+(10)/(6)+10^2-2=20+(5)/(3)+100-2=118+(5)/(3)=(359)/(3)`.

So, the answer is
`\boxed{(359)/(3)}` and we're done!

Answer 2

`{ \rm{2(a + b) + (a + b)/(6) + {(a + b)}^(2) - 2}} \\`

• substitute (a + b) with 10:

`= { \tt{2(10) + (10)/(6) + {(10)}^(2) - 2 }} \\ \\ = { \tt{20 + (10)/(6) + 100 - 2}} \\ \\ { \boxed{ \tt{ = 119 (2)/(3) }}}`