Question 66

If $$a^2 + b^2 + c^2 = 300$$ and $$ab + bc + ca = 50$$, then what is the value of $$a + b + c$$ ? (Given that a, b and c are all positive.)

Solution

$$(a + b + c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca)$$

$$(a + b + c)^2 = 300 + 2(50)$$

$$(a + b + c)^2 = 400$$

a + b + c = 20

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