The minimum value of the sum of real number `a^(-5),a^(-4),3a^(-3),1,a^8,an d a^(10) with a >0` is

The minimum value of the sum of real number a^(-5),a^(-4),3a^(-3),1,a^8,a n da^(10)w i t ha >0 is

The minimum value of the sum of real number a^-5,a^-4,3a^-3,1,a^8 and a^10 with a > 0 is

The sum of two non-zero numbers is 8, the minimum value of the sum of their reciprocals is 1/4 (b) 1/2 (c) 1/8 (d) none of these

The minimum number of real roots of (x^(2)+3x+a)(x^(2)+ax+1)=0 equals

If a ,b ,c are non-zero real numbers, then find the minimum value of the expression (((a^4+ 3a^2+1)(b^4+5b^2+1)(c^4+7c^2+1))/(a^2b^2c^2)) which is not divisible by prime number.

Find the sum of the products of the ten numbers +-1,+-2,+-3,+-4,a n d+-5 taking two at a time.

If a,b,c are non-zero real numbers, then the minimum value of the expression ((a^(8)+4a^(4)+1)(b^(4)+3b^(2)+1)(c^(2)+2c+2))/(a^(4)b^(2)) equals

The minimum value of the function, f(x)=x^(3//2)+x^(-3//2)-4(x+(1)/(x)). For all permissible real values of x is

The real number x when added to its inverse given the minimum value of the sum at x equal to (a) 1 (b) -1 (c) -2 (d) 2

The sum of the real roots of the equation x^(5)-5x^(4)+9x^(3)-9x^(2)+5x-1=0 is