how do i find 2 consecutive integers with a PRODUCT of 462?

Question

so far i've gotten to:
(x)(x+1)=462
then i got: x^2+x=462
i can't figure out what comes next...

Answer 1

Good for you for trying this yourself. I just want to hug you for that!!!

OK, do this:

x(x+1) = 462

x^2 + x = 462

x^2 + x - 462 = 0

then factor:

(x + 22) (x - 21) = 0

So x = 21 or -22

So your two consecutive integers are either:

21,22

or

-22, -21

Answer 2

enable x be the 1st integer. Then the 2d integer is x + a million. Now we multiply them at the same time to get this: x (x +a million) = 462 x² + x = 462 Now pass the consistent on the perfect to the left section, and set the equation equivalent to 0: x² + x - 462 = 0. Now element the equation: (x + 21)(x - 20) = 0.. Set each and each element equivalent to 0 and resolve for x for each element: x + 21 = 0 ----> x = -21 x - 20 = 0 ----> x = 20. This leads us to 2 interesting opportunities. the situation does no longer say that the integers ought to be advantageous or damaging, so we are in a position to easily use the advantageous and damaging value of 20 and 21. If x = 20, then x + a million = 20 + a million = 21, and 20 x 21 = 462. So this answer works. If x = -21, then x + a million = -21 + a million = -20, and -21 x -20 = 462. So this answer works besides. So listed under are the integers: x = -20 and -21, and x = 20 and 21.

Answer 3

The way you have suggested would work and to do it that way you could use the quadratic formula to solve it.
But a simpler way is to think about it for a second ,and then proceed logically. Since the integers are consecutive, try multiplying two consecutive integers which you think are close,
say, 20x21. 20x21=420 too low
Try 24x25=600 too high
So the integers Willl be between 21 and 24.
That's easy; either : 21x22, 22x23 or 23x24
Multiply and see which works.
Well, 21 and 22 are a pair of consecutive integers whose product is 462.

But what about the negative integers?
Two negative integers multiplied together gives a positive result,
so -21 and -22 work as well.

If you use the quadratic formula, watch your minus signs and concentrate on what your answers mean.
If you factor the quadratic, the factors wil be
(x-21)(x+22)or x=21,(-22)
Remember from the start you defined x as the lower integer in the pair, so the pairs you would get from solving the quadratic are 21,22 and
(-22),(-21), just like in the other method.

Answer 4

what you did so far was right...

x^2 + x = 462
x^2 + x - 462= 0
(x+22)(x-21)=0

x= -22 or x=21

so, the two integers are -22, --21 or 21 and 22

Answer 5

21 and 22

Answer 6

x^2+x-462=0

Factor, this can be done many ways one is the quadratic equation....
-b plus/minus Sqrt(b^2-4ac)divided by 2a so
-1 plus/minus Sqrt(1-4*1*-462) divided by 2*1
-1 plus/minus Sqrt(1+1848) divided by 2
-1plus/minus Sqrt(1849) divided by 2
-1plus/minus43 /2

1 plus 43 divided by 2 is 44/2 = 22
1 minus 43 divided by 2 is 42/2=21

21*22=462

Answer 7

it means to find two numbers in a row that the product is 462 in this case it is 21x22 this is how it is done



its like guess and check
19
x 20
________
380-wrong


20
x21
_____
420-close but wrong


21
x 22
_______
462-correct
the numbers have to be in the order like if u count the second # comes right after the first

Answer 8

i'ts 21* 22 if it helps
TO SOLVE
use a calculator to find a sqare root of 462
=21.494185.........
round it down to find the smaller number
round it up to find the greater.

Answer 9

ans:►21,22 or -21,-22