If A+3b=6 And Ab=3, Then The Value Of A^2 +9b^2 Is: - Testpoint

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

2
12
18
None of these

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)

Now square equation (1):

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

Use $ab = 3$

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

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