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Question
Find the consecutive even integers whose squares have the sum 340.
Solution
Let the consecutive even integers be 2x and 2x + 2.
Then according to the given hypothesis,
(2๐ฅ)2 + (2๐ฅ + 2)2 = 340
⇒ 8๐ฅ2 + 8๐ฅ - 336 = 0
⇒ ๐ฅ2 + ๐ฅ - 42 = 0
⇒ ๐ฅ2 + 7๐ฅ - 6๐ฅ - 42 = 0
⇒ ๐ฅ(๐ฅ + 7) - 6(๐ฅ + 7) = 0
⇒ (๐ฅ + 7)(๐ฅ - 6) = 0
⇒ x = -7 or x = 6
Considering, the positive integers of x.
⇒ x = 6; 2x = 12 and 2x + 2 = 14.
∴ The two consecutive even integers are 12 and 14.
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