**If 2a + 3b = 7 and ab = 2, find 4a**^{2} + 9b^{2}.

^{2}+ 9b

^{2}.

**Answer :**

We know that

(2a + 3b)^{2} = 4a^{2} + 9b^{2} + 12ab

It can be written as

4a^{2} + 9b^{2} = (2a + 3b)^{2} – 12ab

It is given that

2a + 3b = 7

ab = 2

Substituting the values

4a^{2} + 9b^{2} = 7^{2} – 12 × 2

By further calculation

= 49 – 24

= 25

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