a and b are two positive integers such that `a^(b)timesb^(a)=800`. Find the a and b.

Can you think of positive integers a, b such that a^(b) = b^(a) ?

If a and b are positive numbers such that a^(2) + b^(2) = 4 , then find the maximum value of a^(2) b .

Let a,b ,c be positive integers such that b/a is an integer. If a,b,c are in GP and the arithmetic mean of a,b,c, is b+2 then the value of (a^2+a-14)/(a+1) is

Let a,b ,c be positive integers such that b/a is an integer. If a,b,c are in GP and the arithmetic mean of a,b,c, is b+2 then the value of (a^2+a-14)/(a+1) is

If a , b are two fixed positive integers such that f(a+x)=b+[b^3+1-3b^2f(x)+3b{f(x)}^2-{f(x)}^3]^(1/3) for all real x , then prove that f(x) is periodic and find its period.

If vec a and vec b are two vectors such that | vec axx vec b|=2, then find the value of [ vec a vec b vec axx vec b].

Statement 1: Let A ,B be two square matrices of the same order such that A B=B A ,A^m=O ,n dB^n=O for some positive integers m ,n , then there exists a positive integer r such that (A+B)^r=Odot Statement 2: If A B=B At h e n(A+B)^r can be expanded as binomial expansion.

If a_(n) and b_(n) are positive integers and a_(n)+sqrt2b_(n)=(2+sqrt2))^(n) , then lim_(nrarroo) ((a_(n))/(b_(n))) =

Let a , b , c , d be positive integers such that (log)_a b=3/2a n d(log)_c d=5/4dot If (a-c)=9, then find the value of (b-d)dot