Application of DerivativeHard

Question

If (1 + 3 + 5 + ...+ a) + (1 + 3 + 5 + ...+ b) = (1 + 3 + 5 + ...+ c), where each set of paren theses contains the sum of consecutive odd integers as shown such that - (i) a + b + c = 21, (ii) a > 6 If G = Max{a, b, c} and L = Min{a, b, c}, then -

Options

A.G - L = 4
B.b - a = 2
C.G - L = 7
D.a - b = 2

Solution

  
(2r - 1) = n2
⇒ a = 2n - 1
⇒ n =
⇒ (a + 1)2 + (b + 1)2 = (c + 1)2
= 8 = 6 = 10      (∵a + b + c = 21)
⇒ a = 7 b = 5 c = 9
Hence G = 9 L = 5
G - L = 4 & a - b = 2

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