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If (a + b)2 = 21 + c2, (b + c)2 = 32 + a2 and (c + a)2 = 28 + b2 , find a + b + c = ?
- A9
- B7
- C6
- D8
Answer not set
Discussion 1
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CCommunity
(a + b)2 - c2 = 21
(a + b + c)(a + b - c) = 21 ------(i)
(b + c)2 - a2 = 32
(a + b + c)(b + c - a) = 32 ------(ii)
(c + a)2 - b2 = 28
(c + a + b)(c + a - b)=28 ------(iii)
Adding all three equations-
(a + b + c)[(a + b + c) + (b + c + a) + (c + a - b)] = 81
(a + b + c)2 = 81
a + b + c = 9
(a + b + c)(a + b - c) = 21 ------(i)
(b + c)2 - a2 = 32
(a + b + c)(b + c - a) = 32 ------(ii)
(c + a)2 - b2 = 28
(c + a + b)(c + a - b)=28 ------(iii)
Adding all three equations-
(a + b + c)[(a + b + c) + (b + c + a) + (c + a - b)] = 81
(a + b + c)2 = 81
a + b + c = 9