Question : If $2a+3b=14$ and $2a-3b=10$, then find the value of ' $ab$ '.
Option 1: 5
Option 2: 3
Option 3: 4
Option 4: 2
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Correct Answer: 4
Solution : Given: $2a+3b=14$.............(1) $2 a-3 b=10$................(2) Squaring both sides and subtract $(2a+3b)^2 - (2a-3b)^2=14^2-10^2$ ⇒ $(4a)^2 + (3b)^2 + 12ab - (4a)^2 - (3b)^2 + 12ab = 96$ ⇒ $24ab=96$ So, $ab=4$ Hence, the correct answer is 4.
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