# Q 98. Least value of z belong to R for which 4zx^2+1/x>=1 for all x>0 is

Vipul Tiwari
21 Points
4 years ago
[4zx^2 + (1/2x0 + (1/2x)]/3 $\geqslant$ [(4zx^2.(1/2x).(1/2x)]^(1/3)
[4zx^2 + (1/2x) + (1/2x)] $\geqslant$3[4zx^2.(1/4x^2)]^(1/3)
4zx^2 + (1/2x) + (1/2x) $\geqslant$3(z)^(1/3)
since its true for all x $>$0,so
3.(z)^1/3$\geqslant$1
(z)^1/3$\geqslant$1/3
z$\geqslant$1/27