Inequalities Involving Mathematical Means
Trending Questions
Q.
If a, b, x, y are positive, then (ab + xy) (ax + by) is
> 2abxy
> 4abxy
2abxy
< 4abxy
Q.
If a, b, c, d are positive numbers, then ab+cd<2√abcd
False
True
Q.
If a2+b2+c2=1, then bc+ca+ab lies in the interval
[-1, 2]
[−12, 1]
[−1, 12]
[−12, 3]
Q.
If roots of the equation
x4−8x3+bx2+cx+16=0
are positive, then
b=8
c=-32
b=24
c=32
Q.
If a, b and c are three positive real numbers, which one of the following are true?
a2+b2+c2≥bc+ca+ab
a3+b3+c3≥3abc
(b+c)(c+a)(a+b)≥8abc
bca+cab+abc≥a+b+c
Q.
Let a, b, c be the sides of a triangle. The least value of expressionE=ab+c−a+bc+a−b+ca+b−c is
Q. If roots of the equation f(x)=x6−12x5+bx4+cx3+dx2+ex+64=0 are positive, then the remainder when f(x) is divided by x-1 is
- 2
- 1
- 3
- 10