Question

The profuct of two consecutive even natural number is 48.find the number numbers.

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

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$\green{\underline \bold{Given :}}$

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• Product of two consecutive even natural number is 48.

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$\red{\underline \bold{To \: Find:}}$

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• The numbers

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$\large{\orange{\underline{\tt{Solution :-}}}}$

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Let us firstly observe some consecutive even natural numbers.

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• 2,4
• 4,6
• 6,8
• 8,10

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Here we can see a similarity in every pair.

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• 2,4 = 2 , 2 + 2
• 4,6 = 4 , 4 + 2
• 6,8 = 6 , 6 + 2
• 8,10 = 8 , 8 + 2

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We got that successive even number can be found by adding 2 to the previous even number.

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Hence,

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Let the first even number be 'x'

So,

Its consecutive even number will be 'x + 2'

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$\purple{\underline \bold{According \: to \: the \ question :}}$

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$\sf \longmapsto (x)(x + 2) = 48$

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$\sf \longmapsto x^2 + 2x = 48$

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$\sf \longmapsto x^2 + 2x - 48 = 0$

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$\underline{\bold{\texttt{Splitting the middle term}}}$

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$\sf \longmapsto x^2 + 8x - 6x - 48 = 0$

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$\sf \longmapsto x(x + 8) -6(x + 8)$

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$\sf \longmapsto (x + 8)(x - 6)$

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$\bf \dashrightarrow x = -8 \: \& \: x = 6$

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$\underline{\bold{\texttt{'x' is a natural number }}}$

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$\purple\longrightarrow$ $\rm x = 6$

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First number is 6 Hence its consecutive number will be '6 + 2'

i.e 8

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The numbers are 6 & 8

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