Which of the following statements must be true about n in the expression for a Mersenne prime, 2nā1
?
3 answers
The expression for a Mersenne prime is 2^šā1. Therefore, the value of n must be a positive integer.
Question
Mei wants to generate a Pythagorean triple when x equals 8 and y equals 6 using the polynomial identity (x^2+y^2)^2=(x^2āy^2)^2+(2xy)^2
. How does she write the Pythagorean triple, in ascending order?
Mei wants to generate a Pythagorean triple when x equals 8 and y equals 6 using the polynomial identity (x^2+y^2)^2=(x^2āy^2)^2+(2xy)^2
. How does she write the Pythagorean triple, in ascending order?
To generate a Pythagorean triple using the polynomial identity (x^2+y^2)^2=(x^2āy^2)^2+(2xy)^2, we can substitute the given values for x and y.
When x = 8 and y = 6, the equation becomes: (8^2 + 6^2)^2 = (8^2 - 6^2)^2 + (2*8*6)^2
Simplifying this equation gives: (64 + 36)^2 = (64 - 36)^2 + (96)^2
This further simplifies to: 100^2 = 28^2 + 96^2
Therefore, the Pythagorean triple can be written as (28, 96, 100) in ascending order.
When x = 8 and y = 6, the equation becomes: (8^2 + 6^2)^2 = (8^2 - 6^2)^2 + (2*8*6)^2
Simplifying this equation gives: (64 + 36)^2 = (64 - 36)^2 + (96)^2
This further simplifies to: 100^2 = 28^2 + 96^2
Therefore, the Pythagorean triple can be written as (28, 96, 100) in ascending order.
1 answer