Why 5X5 is 25 while 4X6 is 24?

Question

I am trying to say, 5x5 is 25. If you multiply 1 less than 5 with one more than 5, you should get the same answer. 5 is the geometrical mean of 4 and 6 .... While I am decreasing one five by 1,,,,,,, I am increasing the other five by 1. therefore the results must be the same

Answer 1

illogical

Answer 2

check_check,
I had noticed that you had asked this question before and I thought of answering because I thought that this what you were thinking.
You are right that 5 is in the middle and you increase by 1 to get six and decrease by one to get 4, but the increase and decrease are not the same percentage. 5 is 25% more than 4, while 6 is only 20% more than 5. So 4x6 will have to be less than 5x5. If you had: (6/5)X times (5/6)X then you'd get X^2. A good geomertical insight is to think of a square with side length X, so the area is X^2.
Now imagine I shorten two opposite sides by amount y, and lengthen the other two sides by by the same amount y. Then the area is now (X-y)(X+y) = X^2 -y^2 so we see that if y is greater than 0, the area will decrease by an amount y^2. Of course the square could have side length 5 and we could let y = 1 and we would have your situation. Factoring 5^2 -1 = (5+1)*(5-1) = 6x4 = 24.
Anyways, I hope this is of some help.

Answer 3

5 is not Geometric mean of 4 and 6.
5 is arithmetis mean of 4 and 6.
Arithmetic mean of a and b is (a+b)/2.
Geometric mean of a and b is sqrt(ab).
(a-1)(a+1)=a^2-1 for any value of 'a'.
4*6=5*5-1
5*7=6*6-1
6*8=7*7-1
what is wrong with your 5x5=25 and 4x5=24?

Answer 4

I think you're partially getting confused with geometric and arithmetic means.. However consider a * a = a^2 = y. Now (a+1)(a-1) = a^2 -1 = y - 1.

Answer 5

(x-1)*(x+1) =(x^2)
expand the left side of the factor
x^2 +x -x -1 becomes x^2 -1

You can see this graphically by drawing a NxN grid. Remove the bottom right corner. You have (N^2 -1) squares. Now move the far right side of the grid(N-1) squares to the bottom row of the grid and you end up with a (N-1)*(N+1) rectangle

Answer 6

who told u that 5 is geometrical mean of 6 & 4..in fact 5 is arithmatic mean of 6&4..the GM of 6&4 is squareroot of (6X4=24).
if u consider it as puzzle then the diff of 4 occured bcoz of..

5*5+(1-1)(5)+(1)(-1) = 24 = (5-1)(5+1)

think it will answer ur question.

Answer 7

the respond is a million. the concern is 5x5=+25 what you do is multiply the fives and you get 25. with the intention to deliver the 25 to the different element of the equivalent sign you ought to divide it. you ought to DIVIDE ON the two aspects so comprehend it appears that evidently like this.=+25/25 and this equals ONE or ought to I say +a million

Answer 8

x*x=x^2 but
(x-1)*(x+1)=x^2+x-x-1=x^2-1
it is not correct that x^2#x^2-1

Answer 9

im not a math genius but that seems like a good question

Answer 10

ask galileo galilee..