1.

The sum of the squares of two consecutive even numbers is 6500. Which is the smaller number?(a) 54 (b) 52(c) 48 (d) 56(e) None of these

Answer»

(d) Let the two numbers be x and (x + 2). 

Then, x2 + (x + 2)2 = 6500 

x2 + x2 + 4x + 4 = 6500 

2x2 + 4x – 6496 = 0 

x2 + 2x – 3248 = 0 

x2 + 58x – 56x – 3248 = 0 

(x + 58) (x – 56) = 0 

x = 56



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