Find 4 consecutive even integers where the product of the two smaller numbers is 72 less than the product of the two larger numbers?

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01-08-2014
Mathematics

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Find 4 consecutive even integers where the product of the two smaller numbers is 72 less than the product of the two larger numbers?

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Anonymous Anonymous · Answer 1 · 2014-08-01T08:50:23-04:00

Anonymous Anonymous

01-08-2014

\(n;\ n+2;\ n+4;\ n+6-numbers\\\ (n+2)+72=(n+4)(n+6)\ ^2+2n+72=n^2+6n+4n+24\ ^2+2n+72=n^2+10n+24\ ^2-n^2+2n-10n=24-72\\-8n=-48\ \ \ \ /:(-8)\ =6\\\\Solutions:\fbox6;\ 6+2=\fbox8;\ 8+2=\fbox{10};\ 10+2=\fbox{12}.\)

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