Question
Let there be two positive even integers such that the difference between them is 4. If their product is 96, find the numbers.
Solution :
Let the one even integer = `x`The other even integer = `x + 4`
Given :
The product of integers = `96`Therefore,
`(x)(x + 4) = 96`
`x^2 + 4x = 96`
`x^2 + 4x - 96 = 0`
Splitting the middle term,
`x^2 + 12x - 8x - 96 = 0`
Factoring out `x + 12`,
`x(x + 12) -8(x + 12) = 0`
`(x + 12) (x - 8) = 0`
By zero product rule,
`x + 12 = 0` or `x - 8 = 0`
`x = -12` `x = 8`
`x = {-12 , 8}`
Answer is x = 8 and x + 4 = 12, so the two positive even integers are 8 and 12.
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