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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