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Sequence & Series Test - 1

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Sequence & Series Test - 1
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  • Question 1
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    If a, b, c are non-zero real numbers such that (a 2+ b 2 + c 2 + 1) = 2 (a + b + c + ab + bc + ca); then

    Solution

    3 (a2+b2+c2+1) - 2 (a + b + c + ab + bc +ca) = 0

    ⇒[(a - b)2 + (b - c)2+ (c - a)2] + [(a - 1)2 + (b - 1)2+ (c - 1)2] = 0

    ⇒a - b = b - c = c - a = 0 

    and a - 1 = b - 1 = c - 1 = 0 

    ⇒a = b = c = 1

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