If `((x-a)(x-b))/((x-c)(x-d)^2) ge0;` where `a gt b gtc ge d gt 0,` then `x in`

The least positive integeral value of real lambda so that the equation (x-a)(x-c)(x-e)+lambda (x-b)(x-d)=0, (a gt b gt c gt d gt e) has distinct real roots is __________.

The least positive integeral value of real lambda so that the equation (x-a)(x-c)(x-e)+lambda (x-b)(x-d)=0, (a gt b gt c gt d gt e) has distinct real roots is __________.

If ax^(2)+b/x ge c, AA x gt0 , where agt0,bgt0 then

x+y le 9. y gt x, x ge 0

x+y le 9. y gt x, x ge 0

Using calculus establish the inequality, (x^(b)+y^(b))^(1//b) lt ( x^(a)+y^(a))^(1//a) , where x gt 0 , y gt 0 and b gt a gt 0 .