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

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

Question Image
Grade:12

1 Answers

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)] \geqslant3[4zx^2.(1/4x^2)]^(1/3)
4zx^2 + (1/2x) + (1/2x) \geqslant3(z)^(1/3)
since its true for all x >0,so
3.(z)^1/3\geqslant1
(z)^1/3\geqslant1/3
z\geqslant1/27

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