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Question
If a2 + b2 + c2 = 50 and ab + bc + ca = 47, find a + b + c.
Sum
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Solution
a2 + b2 + c2 = 50 and ab + bc + ca = 47
Since ( a + b + c )2 = a2 + b2 + c2 + 2( ab + bc + ca )
∴ ( a + b + c )2 = 50 + 2(47)
⇒ ( a + b + c )2 = 50 + 94 = 144
⇒ a + b +c = `sqrt144 = +- 12`
∴ a + b + c = `+-12`
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Expansion of Formula
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