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Question
Find the two consecutive positive even integers whose product is 288.
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Solution
Let the two consecutive positive even integers be x and(x+2)
According to the given condition,
`x(x+2)=288`
⇒`x^2+2x-288=0`
⇒`x^2+18x-16x-288=0`
⇒`x(x+18)-16(x+18)=0`
⇒`(x+18)(x-16)=0`
⇒`x+18=0 or x-16=0`
⇒`x=-18 or x=16`
`∴x=16 ` (x is a positive even integer)
When` x=16 `
`x+2=16+2=18`
Hence, the required integers are 16 and 18.
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