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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.​

 Feb 18, 2020
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Let the two smallest  integers =  x  and x + 2

 

Let the two largest  =  x + 4 , x + 6

 

So

 

x(x + 2) + 72  = (x + 4) ( x + 6)       simplify

 

x^2 + 2x  + 72 =  x^2  + 4x + 6x  + 24      subtract x^2 from both sides and simplify

 

2x + 72  =  10x  + 24     subtract  24, 2x from both sides

 

8x  =  48   divide both sides by 8

 

x = 6

 

x + 2  =8

 

x + 4  =10 

 

x + 6  = 12

 

 

cool cool cool

 Feb 18, 2020

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