Given that the product of 22 integers is equal to 1, prove that their sum is not equal to 0.

Fun problem.

We have a positive product, so no zero factors.

We have a positive product, so an even number of negative factors.

We have a product of 1, so all the integers must be either +1 or -1.

If we have 2n factors of -1 we have 22-2n factors of 1 so a sum of

For that to be zero we need

That's not an integer; we've shown there's no even number of -1s that will make the sum zero, and since there must be an even number of -1s, the sum cannot equal zero.

the answer is a

step-by-step explanation:

answer

d. 10

explanation

the distance from point y to wx is the height of the triangle.

using pythagoras theorem,

group similar terms to get,

this implies that,

take positive square root of both sides to get,

this implies that,