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Find two consecutive positive even numbers the sum of whose squares is 340?
Wiki User
∙ 13y ago
Let the number be 'm' & 'm + 2'
Hence their squares are m^2 & (m+2)^2
There sum is
m^2 + (m+2)^2 = 340
Multiply out he brackets
m^2 + m^2 + 4m + 4 = 340 .
2m^2 + 4m + 4 = 340
Divide both sides by '2'
m^2 + 2m + 2 = 170
m^2 + 2m - 168 = 0
Factor
(m - 12)(m + 14) = 0
Hence m = 12 & m+ 2 = 14 The two consecutive even numbers.
12^2 = 144
14^2 = 196
144 + 196 = 340 As required.
lenpollock
Wiki User
∙ 13y ago122 + 142 = 340
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