Remark
We have to assume that there are only 3 consecutive integers.
Givens
Let the smallest integer = x
Let the middle integer = x + 1
Let the largest integer = x + 2
Formulas
4(x + 2)^2 - 3x^2 = 41+ 2*(x + 1)^2 Expand the brackets.
Solution
4(x^2 + 4x + 4) - 3x^2 = 41 + 2(x^2 + 2x + 1) Remove the brackets.
4x^2 + 16x + 16 - 3x^2 = 41 + 2x^2 + 4x + 2 Collect like terms on both sides
x^2 + 16x + 16 =2x^2 + 4x + 43 Subtract the left side from the right
0 = 2x^2 - x^2 - 16x + 4x - 16 + 43 Collect like terms.
0 = x^2 - 12x + 27 This factors
(x - 3) * (x - 9) = 0
x - 3 = 0
x = 3 or
x - 9 = 0
x = 9
Therefore numbers can be 3,4,5 or 9,10,11
We need to check both.
First group check.
Group One
4*5^2 - 3*3^2 = 41 + 2*4^2
4*25 - 3*9 = 41 + 2*16
100 - 27 = 41 + 32
73 = 73
Group one is correct.
Group Two
4*11^2 - 3*9^2 = 41 + 2*10^2
484 - 243 = 41 + 200
241 = 241 and the second group checks as well. So thee are two sets of answers.
3,4,5 and 9,10,11 <<<<<< Answer.
Note: You should put this in math.
Saltation - During wind erosion, wind carries loose material from the bed, but transports it back to the surface later. This can be done by any fluid, like water too. Other examples of saltation include transport of pebbles by river and snow drifting over smooth surfaces in the Arctic.
