if `x, y, r` and `s` are positive real no’s. such that `x² + y² =r^2+s^2 = 1,` then max value of `xr+ys`

if x,y,r and s are positive real no's.such that x^(2)+y^(2)=r^(2)+s^(2)=1, then max value of xr+ys

Consider the following S_(1) : Let a _(1),a_(2),a_(3),...a_(8) be 8 non-negative real numbers such that a_(1)+a_(2)+a_(3)+.....+a_(8)=16 and P =a_(1)a_(2)+a_(2)a_(3)+a_(3)a_(4)+...+a_(7)a_(8), then the maximum value of P is 64. S_(2) : If x,y,r,s in R+ such that x^(2)+y^(2)=r^(2)+s^(2)=1 ,then the maximum value of (xr+ys) is 2 . S_(3) : If A.M .and G.M between two positive numbers are respectively A and G ,then the numbers are A+sqrt(A^(2)-G^(2)), A-sqrt(A^(2)-G^(2)) S_(4) : If p,q,r be 3 distinct real numbers in A.P. then p^(3)+r^(3) equals -6pqr

If r and s are roots of x^(2) + px + q = 0 , then what is the value of (1//r^(2))+ ( 1//s^(2)) ?

If x,y,z are all positive real number and x+y+z=s ,then prove that (s-x)(s-y)(s-z)ge8xyz .

Q.34 Q.34 Show that the roots r,s and t of the cubic Show that the roots r,s and t of the cubic x(x-2) (3x-7) 2, are real and positive. Also compute the value of tan-(r) + tan-(s) + tan (t) the value oftan ()+ tan(s)+ tan(0)

Let a function f: R to R , where R is the set of real nos. satisfying the equation f(x+y) = f(x) + f(y) AA x, y if f(x) is continuous at x = 0, then

The operation & is defined as r & s =(s^(2)-r^(2))/(r+s) where r and s are real number and r ne -s . What is the value of 3 & 4?

R and S are brothers, X is the sister of Y and X is the mother of R. What is Y to S?