If `a , b` are two real numbers with a`<`b then a real number `c` can be found between `a and b` such that the value of `(a^2+a b+b^2)/(c^2)i s_____`

If x and are two real numbers, then prove by mathematical induction that (x^(n)-y^(n)) is divisible by (x-y) for all ninNN .

Let a and b be two real numbers such that a > 1, b >1. If A=((a,0),(0,b)), then (lim)_(n->oo) A^-n is (a) unit matrix (b) null matrix (c) 2I (d) non of these

If a , b , c are real numbers forming an A.P. and 3+a , 2+b , 3+c are in G.P. , then minimum value of ac is

If a and b be two real numbers and b > 0. then which one of the followings is false ?

If a,b,c, are non-zero real numbers, then the inverse of matrix A = [(a,0,0),(0,b,0),(0,0,c)] is -

If a, b, c, are real numbers such that |{:(b+c,c+a,a+b),(c+a,a+b,b+c),(a+b,b+c,c+a):}|=0, then show that either a+b+c=0 or, a=b=c.

If the argument of (z-a)(barz-b) is equal to that ((sqrt(3)+i)(1+sqrt(3)i)/(1+i)) where a,b,c are two real number and z is the complex conjugate o the complex number z find the locus of z in the rgand diagram. Find the value of a and b so that locus becomes a circle having its centre at 1/2(3+i)

If a,b,c are positive real number, then the least value of (a+b+c)(1/a+1/b+1/c) is