There are 5 consecutive odd numbers. If the difference between the square of the average of the first two odd numbers and square of the average of the last two odd numbers is 492, what is the smallest odd number ?
Let the five consecutive odd numbers = $$(x - 4) , (x - 2) , (x) , (x + 2) , (x + 4)$$
Average of first two numbers = $$\frac{(x - 4) + (x - 2)}{2} = (x - 3)$$
Average of last two numbers = $$\frac{(x + 4) + (x + 2)}{2} = (x + 3)$$
Acc. to ques, => $$(x + 3)^2 - (x - 3)^2 = 492$$
=> $$(x^2 + 9 + 6x) - (x^2 + 9 - 6x) = 492$$
=> $$6x + 6x = 12x = 492$$
=> $$x = \frac{492}{12} = 41$$
$$\therefore$$ Smallest odd number = $$x - 4 = 41 - 4 = 37$$
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