SOLUTION: 1. The operation ⊙ is defined by (2a+b)⊙(a+2b)=a2+ab+b2. Find 6⊙9. (show solution)

Algebra ->  Test -> SOLUTION: 1. The operation ⊙ is defined by (2a+b)⊙(a+2b)=a2+ab+b2. Find 6⊙9. (show solution)      Log On


   

Question 1175602: 1. The operation ⊙ is defined by (2a+b)⊙(a+2b)=a2+ab+b2. Find 6⊙9. (show solution)
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Note: Use "^" to denote exponentiation -- e.g., "a^2" instead of just "a2".

You are given the definition

(2a+b)⊙(a+2b)=a^2+ab+b^2

You are asked to evaluate 6⊙9.

In this example, the operation is not defined in terms of numbers; it is defined in terms of algebraic expressions. So you first need to find what the numbers a and b are.

Being asked to evaluate 6⊙9, you know that (2a+b) is 6 and (a+2b) is 9. So

2a%2Bb=6
a%2B2b=9

One way to solve this particular pair of equations is to add the two equations:

3a%2B3b=15
a%2Bb=5

Then that equation, together with the two original equations, quickly tells us a=1 and b=4.

Now we can use those values to evaluate 6⊙9.

6⊙9 = a^2+ab+b^2 = 1^1+1*4+4^2 = 1+4+16 = 21