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Question
The sum of the squares of two consecutive positive even numbers is 452. Find the numbers.
Solution
Let the two consecutive positive even numbers be x and x 2.
According to the given condition,
`x^2+(x+2)^2=452`
⇒`x^2+x^2+4x+4=452`
⇒`2x^2+4x-448=0`
⇒`x^2+2x-224=0`
⇒`x^2+16x-14x-224=0`
⇒`x(x-16)-14(x-16)=0`
⇒`(x+16)(x-14)=0`
⇒`x+16=0 or x-14=0`
⇒`x=-16 or x=14`
∴ `x=14` (x is a positive even number)
When `x=14`
`x+2=14+2=16`
Hence, the required numbers are 14 and 16.
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