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Find all pairs of consecutive even posit...

Find all pairs of consecutive even positive integers, both of which are larger than 5, such that their sum is less than 23.

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Let x and x + 2 are consecutive even numbers. Sum of number `= x + (x +2) = 2x + 2`
According to the problem , `2x + 2 lt 23`
`rArr 2x lt 21 `
`rArr x lt (21)/(2)`
`rArr x lt 10.5`
But `x gt 5 `
` :' x gt 5 and x lt 10.5 `
`rArr 5 lt x lt 10.5 `
`rArr x = 6 or 8 or or 10`
`rArr x + 2 = 8 or 10 or 12`
Therefore possible pairs of consecutive even numbers are (6, 8 ) , (8, 10).
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