Question

Let x, y, z be three irrational numbers. Show that there are two of them whose...

Let x, y, z be three irrational numbers. Show that there are two of them whose sum is again irrational.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

First, we will show that the sum or difference of two irrational numbers can be rational.

√3 + (-√3) is the sum of irrationals, and the sum is rational.

Therefore, the sum or difference of two irrational numbers can be rational.

Now, whenever a third distinct irrational term is added to these two terms, the sum is irrational.

Consequently, whenever the third irrational term is added to any of the previous two terms, the sum is irrational.

Therefore, there are two of them whose sum is again irrational.

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Find two + numbers x and y whose product xy is 8 and whose sum is...
Find two + numbers x and y whose product xy is 8 and whose sum is 2x+y is a minimum  
Show that if a,y,z are rational numbers such that x < y and y < z,...
Show that if a,y,z are rational numbers such that x < y and y < z, then x < z.
Let p and q be irrational numbers. Is p−q rational or irrational? Show all proof.
Let p and q be irrational numbers. Is p−q rational or irrational? Show all proof.
Three numbers x, y, and z that sum to 99 and also have their squares sum...
Three numbers x, y, and z that sum to 99 and also have their squares sum to 99. By Lagrange method, find x, y, and z so that their product is a minimum.
Find two positive numbers x and y whose sum is 7 so that x^(2)*y−8x is a...
Find two positive numbers x and y whose sum is 7 so that x^(2)*y−8x is a maximum.
1. Consider the following optimization problem. Find two positive numbers x and y whose sum is...
1. Consider the following optimization problem. Find two positive numbers x and y whose sum is 50 and whose product is maximal. Which of the following is the objective function? A. xy=50 B. f(x,y)=xy C. x+y=50 D. f(x,y)=x+y 2. Consider the same optimization problem. Find two positive numbers x and y whose sum is 50 and whose product is maximal. Which of the following is the constraint equation? A. xy=50 B. f(x,y)=xy C. x+y=50 D. f(x,y)=x+y 3. Consider the same...
Let x = {x} and y ={y} represent bounded sequences of real numbers, z = x...
Let x = {x} and y ={y} represent bounded sequences of real numbers, z = x + y, prove the following: supX + supY = supZ where sup represents the supremum of each sequence.
Definition:In the complex numbers, let J denote the set, {x+y√3i :x and y are in Z}....
Definition:In the complex numbers, let J denote the set, {x+y√3i :x and y are in Z}. J is an integral domain containing Z. If a is in J, then N(a) is a non-negative member of Z. If a and b are in J and a|b in J, then N(a)|N(b) in Z. The units of J are 1, -1 Question:If a and b are in J and ab = 2, then prove one of a and b is a unit. Thus,...
(1) Let x be a rational number and y be an irrational. Prove that 2(y-x) is...
(1) Let x be a rational number and y be an irrational. Prove that 2(y-x) is irrational a) Briefly explain which proof method may be most appropriate to prove this statement. For example either contradiction, contraposition or direct proof b) State how to start the proof and then complete the proof
Show the following: a) Let there be Y with the cumulative distribution function F(y). Let F(Y)=Z....
Show the following: a) Let there be Y with the cumulative distribution function F(y). Let F(Y)=Z. Show that Z~U(0,1) for F(y). b) Let X~U(0,1), and let Y := -ln(X). Show that Y~exp(1)
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT