Question

the product of four consecutive positive integers is 840 find the largest number




answer me fast

Answer 1

Let x be the average of the four consecutive positive integers. x is a fraction that has 0.50 as its decimal part.

Then the numbers are:    x-1.5,  x-0.5,  x+0.5, x+1.5

Product:   (x-1.5)(x+1.5) (x-0.5)(x+0.5) = 840

                (x² - 2.25) (x² - 0.25) = 840

                x⁴ - 2.50 x² -  839.4375

                x² =  [2.50 +- √(2.50² + 4*839.4375) ] /2

                    =  [ 2.50 +- 58] /2

                    =  30.25

                x = 5.5

So the numbers are = 4, 5, 6, 7

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It can be done by factorization also:

840 = 2 * 2 * 10 * 21 = 2*2*2*3*5*7

                               = *4*5*6*7

            by rearranging the factors.

Answer 2

840 = a + a + 1 + a + 2 + a + 3

840 = 4 a + 6

840 - 6 = 4 a

834/4 = a

208.5 = a

a + 3 = 211.5

211.5