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What is the proof that a and b are positive numbers and a is greater than b then a squared is greater than b squared?
One way to prove this is as follows:
Given a > b and a>0 and b>0
Define a new constant 'n' such that a - b = n
then a2 = (b + n)2
a2 = b2 + 2bn + n2
since b and n are both positive, 2bn is a positive value and n2 is also positive
So a2 > b2 because a2 - 2bn - n2 = b2
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What is the answer to a squared plus b squared and what's the proof?
Something's missing...
Which number is greater 8.4 or 0.085?
8.4 is greater (larger).0.085 is less than 1. 8.4 is more than 1. 8.4 must therefore be larger.We can prove it is larger by dividing 8.4 by 0.085. If our answer is greater than 1 then it must be larger. This is true for any two positive numbers.8.4 / 0.085 = 98.824 (to 3 decimal places only). This is proof that we are correct.
Determine with proof the set of all prime numbers that can divide 2 successive integers of the form n squared plus 3 where n is a positive integer?
if divides both and , then it will also divide therefore will divide thus The last part comes from the fact that: if gcd(x,y)=g, then . As proof: Since g|x and g|y, let x=kg, and y=jg, then we have so g|(mx+ny).
Why is it that any integer greater than 1791 can be expressed as a sum of at most four hexagonal numbers while integers less than that such as 10 are the sum of 5 hexagonal numbers?
Legendre's proof relating to Hexagonal Numbers and the significance of the number 1791 has been improved upon by Duke and Schulze-Pillot (1990) to just three hexagonal numbers for every sufficiently large integer. There are 13 positive integers within the range 5 to 130 that cannot be represented by only 4 hexagonal numbers. Only the integers 11 and 26 require 6 hexagonal numbers. This is quite a technical subject and source material can be viewed at the link below.
What was Fermat's original proof of his last theorem?
Fermat's last theorem says there does not exist three positive integers a, b, and c which can satisfy the equation an + bn = cn for any integer value of n greater than 2. (2 with be pythagoran triples so we don't include that) Fermat proved the case for n=4, but did not leave a general proof. The proof of this theorem came in 1995. Taylor and Wiles proved it but the math they used was not even known when Fermat was alive so he could not have done a similar proof.
What is the easiest proof in Pythagorean proof?
That for any right angle triangle when its hypotenuse is squared it is equal to the sum of its squared sides.
What is the answer to a squared plus b squared and what's the proof?
Something's missing...
Who originally wrote the proof of a squared plus b squared equals c squared?
Pascal
What is the proof of the Pythagoren Therom?
Look it up on Wikipedia.... the equation is a(squared)+b(squared)=c(squared) multiply the base by the hypotenuse to find the answer
Which number is greater 8.4 or 0.085?
8.4 is greater (larger).0.085 is less than 1. 8.4 is more than 1. 8.4 must therefore be larger.We can prove it is larger by dividing 8.4 by 0.085. If our answer is greater than 1 then it must be larger. This is true for any two positive numbers.8.4 / 0.085 = 98.824 (to 3 decimal places only). This is proof that we are correct.
When was Proof Positive - Greene story - created?
Proof Positive - Greene story - was created in 1930.
Can we include irrational numbers in the set of positive numbers?
Yes, any positive number is a number that doesn't have a (-) behind it (-20; -23.67; -45.45454...), and is not zero (0). Any repeating number (see 3rd negative example) is irrational, no matter what its sign. Irrational numbers also include numbers (decimals, specifically) that don't repeat, but don't stop. Numbers that don't terminate include pi. Pi, as it is, is proof of a positive irrational number.
Determine with proof the set of all prime numbers that can divide 2 successive integers of the form n squared plus 3 where n is a positive integer?
if divides both and , then it will also divide therefore will divide thus The last part comes from the fact that: if gcd(x,y)=g, then . As proof: Since g|x and g|y, let x=kg, and y=jg, then we have so g|(mx+ny).
What actors and actresses appeared in Positive Proof - 1912?
The cast of Positive Proof - 1912 includes: Harry Cashman as Tom Morgan
Could someone help me find some information on a colt police positive 38 special ctg the numbers are 25518r it looks to have an f under the numbers?
Based on the serial # , it was produced in 1978. The funder the numbers could be the proof mark.
What are the release dates for Proof Positive Evidence of the Paranormal - 2004?
Proof Positive Evidence of the Paranormal - 2004 was released on: USA: 6 October 2004
What kinds of numbers would I multiply by to get answers that are slightly less than my starting number A lot less?
NO for Integers NO for Real Numbers proof 1 * any integer is not bigger than that integer nor is 0 * any integer. proof for Real Numbers is easier any real < 1 * any real > 0 is not larger than the second Real for example .5 * 1 = .5 is less than 1 or .5 * 2 = 1 less than 2 or .5 * = 1 less than 2 or -1 *3 = -3 less than 3 so all fractions times a positive Real is less than that positive Real All negative numbers times a positive Real is less than that positive Real and 0 or 1 times all positive Reals is also less than that positive Real NO NO NO is the answer
