Home
Class 12
MATHS
Consider the following S(1) : Let a (1...

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`

Promotional Banner

Similar Questions

Explore conceptually related problems

If a_(1),a_(2),a_(3),a_(4) are positive real numbers such that a_(1)+a_(2)+a_(3)+a_(4)=16 then find maximum value of (a_(1)+a_(2))(a_(3)+a_(4))

Let a_(1),a_(2)…,a_(n) be a non-negative real numbers such that a_(1)+a_(2)+…+a_(n)=m and let S=sum_(iltj) a_(i)a_(j) , then

If a_(1),a_(2),a_(3),.....a_(n) are in H.P.and a_(1)a_(2)+a_(2)a_(3)+a_(3)a_(4)+......a_(n-1)a_(n)=ka_(1)a_(n) then k is equal to

If a_(1),a_(2),a_(3),a_(4),a_(5) are in HP, then a_(1)a_(2)+a_(2)a_(3)+a_(3)a_(4)+a_(4)a_(5) is eqiual to

a_(1),a_(2),a_(3)...,a_(n) are in A.P.such that a_(1)+a_(3)+a_(5)=-12 and a_(1)a_(2)a_(3)=8 then:

a_(1),a_(2),a_(3),......,a_(n), are in A.P such that a_(1)+a_(3)+a_(5)=-12 and a_(1)a_(2)a_(3)=8 then

(a_(1))/(a_(1)+a_(2))+(a_(3))/(a_(3)+a_(4))=(2a_(2))/(a_(2)+a_(3))

If a_(1),a_(2),a_(3),...,a_(100) are in A P such that a_(1)+a_(3)+a_(4)+a_(3)+a_(7)=20 then a_(4)=

If a_(1),a_(2),a_(3), . . .,a_(n) are non-zero real numbers such that (a_(1)^(2)+a_(2)^(2)+ . .. +a_(n-1).^(2))(a_(2)^(2)+a_(3)^(2)+ . . .+a_(n)^(2))le(a_(1)a_(2)+a_(2)a_(3)+ . . . +a_(n-1)a_(n))^(2)" then", a_(1),a_(2), . . . .a_(n) are in