If 2a + 3b = 10 and ab = 3, then find the value of $$4a^2+9b^2$$​​

Given: 

2a + 3b = 10 

ab = 3 

To find: $$4a^2+9b^2$$ 

Formula Used: 

​$$(a+b)^2 = a^2 + b^2 + 2\cdot a \cdot b$$​​

Solution: 

Squaring 2a + 3b = 10 

​$$(2a+3b)^2 = (10)^2 \\ 4a^2 + 9b^2 +2 \times 2a \times3b = 100 \\ 4a^2 + 9b^2 = 100 - 12a b \\ 4a^2 +9b^2 = 100 - 12 \times 3 \\ 4a^2 + 9 b^2 = 100 - 36 \\ 4a^2 + 9b^2 =\bf 64$$​​​​