If a and b are two odd positive integers...

If a and b are two odd positive integers such that a>b. Then prove that one of the two numbers `(a+b)/2` and `(a-b)/2` is odd and other is even.

REAL NUMBERS
KALYANI PUBLICATION|Exercise Exercise|12 Videos
QUADRATIC EQUATION
KALYANI PUBLICATION|Exercise EXERCISE|144 Videos
RECAPITULATION OF RATIONAL AND IRRATIONAL NUMBERS
KALYANI PUBLICATION|Exercise EXERCISE|20 Videos

Similar Questions

Explore conceptually related problems

If A and G are the AM and GM of the positive number a and b then prove that AgeG

If a and b are positive integers such that a=x^3y^2 and b=xy^3 ,where x,y are prime number then HCF (a,b) is

If p and q are positive integers such that p=ab^2 and q=a^3b ,where a,b are prime numbers then LCM (p,q) is

If a and b are two unequal positive real numbers,then prove that (a+b)(5/a+1/(5b))gt4 .

If A and B are two finite sets,then prove that n(A uu B)=n(A)+n(B)-n(AnnB)

If A and B are two matrices such that AB =B and BA =A, then find the value of A^(2)+B^(2) .

If a,b,c are three positive numbers,then . a/b + b/c + c/a

Prove any one of the following: Ann(A' uu B)=A nn B

If a,b,c are positive unequal real numbers then prove that (a+b+c)(1/a+1/b+1/c)gt9

For some positive integer m,every positive even integer is of the form a)m-1 b)m+1 c)2m d)2m+1