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Algebra puzzle (34) |  |
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Problem
Given is:a + b + c + d = 4
ab + ac + ad + bc + bd + cd = -7
Calculate:
a2 + b2 + c2 + d2
Solution
(a + b + c + d)2 = a2 + b2 + c2 + d2 + 2(ab + ac + ad + bc + bd + cd) = 16
a2 + b2 + c2 + d2 = 16 - 2(-7) = 30
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Problem Given is:a + b + c + d = 4 ab + ac + ad + bc + bd + cd = -7 Calculate: a2 + b2 + c2 + d2 Solution (a + b + c + d)2 = a2 + b2 + c2 + d2 + 2(ab + ac + ad + bc + bd + cd) = 16 a2 + b2 + c2 + d2 = 16 - 2(-7) = 30
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