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Sticky Note
If a+3b=6 and ab=3, then the value of a^2 +9b^2 is:
  1. 2
  2. 12
  3. 18
  4. None of these
Explanation

If
a + 3b = 6 and , then the value of a2+9b2a^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=62=36⇒a2+9b2+6ab=36(a + 3b)^2 = 6^2 = 36 Rightarrow a^2 + 9b^2 + 6ab = 36

Use ab=3ab = 3

a2+9b2+6(3)=36⇒a2+9b2+18=36⇒a2+9b2=18a^2 + 9b^2 + 6(3) = 36 Rightarrow a^2 + 9b^2 + 18 = 36 Rightarrow a^2 + 9b^2 = 18

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