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 a gt b gt 0 are two real numbers, the value of, sqrt(ab+(a-b)sqrt(ab+(a-b)sqrt(ab+(a-b)sqrt(ab+….)))) is

Statement-1: The equation (pi^(e))/(x-e)+(e^(pi))/(x-pi)+(pi^(pi)+e^(e))/(x-pi-e) = 0 has real roots. Statement-2: If f(x) is a polynomial and a, b are two real numbers such that f(a) f(b) lt 0 , then f(x) = 0 has an odd number of real roots between a and b.

If a and b are real numbers, with a gtb and |a| lt|b| , then

If a and b are two real number lying between 0 and 1 such that z_1=a+i, z_2=1+bi and z_3=0 form anequilateral trilangle , then (A) a=2+sqrt(3) (B) b=4-sqrt(3) (C) a=b=2-sqrt(3) (D) a=2,b=sqrt(3)

If a and b are two real number lying between 0 and 1 such that z_1=a+i, z_2=1+bi and z_3=0 form an equilateral triangle , then (A) a=2+sqrt(3) (B) b=4-sqrt(3) (C) a=b=2-sqrt(3) (D) a=2,b=sqrt(3)

For a complex number Z, if the argument of (Z-a)(barZ-b) is (pi)/(4) or (-3pi)/(4) (where a, b are two real numbers), then the value of ab such that the locus of Z represents a circle with centre (3)/(2)+(i)/(2) is (where, i^(2)=-1 )

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 are positive real numbers, then |x|le a hArr

Statement-1: If a, b are positive real numbers such that a^(3)+b^(3)=16 , then a+ble4. Statement-2: If a, b are positive real numbers and ngt1 , then (a^(n)+b^(n))/(2)ge((a+b)/(2))^(n)

If a,b,c are positive real numbers, then the number of real roots of the equation ax^2+b|x|+c is