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Using Cauchy Schwartz equation:
(x^2 + 4y^2 + 9z^2) * (1 + 1/2^2 + 1/3^2) > (x+y+z)^2
(x^2 + 4y^2 + 9z^2) * (49/36) > 14^2
x^2 + 4y^2 + 9z^2 > 144
least value of x^2 + 4y^2 + 9z^2 if x+y+z=14
approach plz
if the roots of the equation x^10 - 1 = 0 are 1 ,a,b,c, ...
find the value of (1-a)(1-b)(1-c) ...
approach plz .......
In how many ways can 4 persons be chosen from a row of 10 persons such that no two persons chosen are sitting next to each other?
(a) 210 (b) 35 (c) 72 (d) None of these
approach plz
Basically we are looking for sum of all natural numbers less than 90 and coprime to 90
So, it will be E(90)*90/2 = 24*90/2 = 1080
=> Sum of all such x/90 = 1080/90 = 12
find the sum of all rational numbers x/90 which are less than 1 and such that HCF(x,90)=1
10
12
15
24
approach plz