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First we can solve for y by factoring it out: y(x+1)+x=30, so y=(30-x)/(x+1)= -1+31/(x+1). Let's start by assuming x and y are positive integers and look for a logical contradiction. Since y is positive, the right side (30-x)/(x+1) must be positive. Since x (and therefore x+1) is positive, 30-x must be positive. Therefore x is less than 31. But hold on! Since y is an integer, y+1=31/(x+1) is an integer. Since 31 is only divisible by 1 and 31, y+1 is an integer implies that (x+1) is 1 or 31, making x either 0 or 30. However, x is positive and less 30, which is impossible! There it cannot be the case that x and y are both positive integers.
AnswerIt's not as complicated as that. Just add 1 to both sides and factorise, and you get: (x+1)(y+1) = 31. Since 31 is prime, one of its factors must be either 1 or -1. So we'd get x+1=1 (so x=0) or else x+1=-1 (so x=-2), or else y=0 or y=-2. But the question says x and y have to be positive.
What else can I help you with?
Determine which postulate or theorem can be used to prove that lmn equals PMN?
SAS
Prove that the order of an element of a group of finite order is a divisor of the order of the group?
Let ( G ) be a finite group with order ( |G| ), and let ( g \in G ) be an element of finite order ( n ). The order of ( g ), denoted ( |g| ), is the smallest positive integer such that ( g^k = e ) for some integer ( k ), where ( e ) is the identity element. The subgroup generated by ( g ), denoted ( \langle g \rangle ), has order ( |g| = n ). By Lagrange's theorem, the order of any subgroup divides the order of the group, thus ( |g| ) divides ( |G| ).
Matrix prove if Ax equals Bx then A equals B?
If x is a null matrix then Ax = Bx for any matrices A and B including when A not equal to B. So the proposition in the question is false and therefore cannot be proven.
If A-B equals null set then prove A subset of B?
A - B is null.=> there are no elements in A - B.=> there are no elements such that they are in A but not in B.=> any element in A is in B.=> A is a subset of B.
Math help can anyone show you how to do this please Prove or disprove that if a and b are rational number then ab is rational?
To prove a number ab is rational, you have to find two integers t and n such that t/n = ab.Since we know that a, and b are rational, they can be expressed as follows:a = p1/q1b = p2/q2then ab = p1p2/q1q2Since p1, p2, q1, and q2 are all integers, p1p2 is an integer, and q1q2 is an integer. This gives us the t, and n we are looking for. t = p1p2 and n = q1q2, and ab = t/n, so ab is rational.
What is proof by induction?
Mathematical induction is just a way of proving a statement to be true for all positive integers: prove the statement to be true about 1; then assume it to be true for a generic integer x, and prove it to be true for x + 1; it therefore must be true for all positive integers.
Do Prove that the product of an integer and arbitrary integer is even?
The statement is not true. Disprove by counter-example: 3 is an integer and 5 is an integer, their product is 15 which is odd.
Is the square root of a 143 a irrational number?
Yes. The square root of a positive integer can ONLY be either:* An integer (in this case, it isn't), OR * An irrational number. The proof is basically the same as the proof used in high school algebra, to prove that the square root of 2 is irrational.
Prove that 2 divided by10 equals 2?
Cannot prove that 2 divided by 10 equals 2 because it is not true.
How can you prove that 1 plus 1 equals 3?
You can't it equals 2. You can't it equals 2.
Can you mathematically prove 9 plus 10 equals 21?
No you can not prove that 9 +10 = 21.
Can you prove the 0 is a real number?
Yes. 0 is an integer and all integers are real numbers.
Can someone prove that 2k 2k 1-1?
You can prove that 2K,2K,1-1 by first determining that the integer N can be written in the form of N=2K.
Prove integer and rational are not homomorphism?
They are! Consider the identity map from Z to Q. They are not isomorphic, but there is a homomorphism between them.
Love equal what?
No, but there is a way to prove that zero equals one.
How can you prove that 1 equals 3?
Using faulty logic.
How do you use inductive reasoning to prove the product of an odd integer and an even integer will always be even?
The product of an odd and even number will always have 2 as a factor. Therefore, it will always be even.
