Explanation

If $a + 3b = 6$ and $ab=3$, then the value of $a^2 + 9b^2$ is:

We are given:

a+3b=6(1),ab=3(2)

$$$$a+3b=6(1),ab=3(2)

Now square equation (1):

$$(a + 3b)^2 = 6^2 = 36 Rightarrow a^2 + 9b^2 + 6ab = 36$$

Use $ab = 3$

$$a^2 + 9b^2 + 6(3) = 36 Rightarrow a^2 + 9b^2 + 18 = 36 Rightarrow a^2 + 9b^2 = 18$$