Basic Inequality - 3

Algebra Level 4

If $x, y, z$ are real numbers, such that $x^2 + y^2 + z^2 = 1$ then find the maximum value of $xy^{2}z^{3}$ .

Give answer to 3 decimal places.

0.098 0.048 0.639 0.056

2 solutions

Raj Rajput
Dec 23, 2015

this is exactly what I did :)

Atul Shivam - 5 years, 5 months ago

Exactly same method!!

But cannot one apply Jensen's inequality?

Priyanshu Mishra - 5 years, 5 months ago

Can you show us how it's done? thanks

Pi Han Goh - 5 years, 5 months ago

I did by the method of AM-GM as done by Raj Rajput.

I want solution by jensen's inequality.

Priyanshu Mishra - 5 years, 5 months ago

Atul Shivam
Dec 24, 2015

hint: apply weighted A.M-G.M method. :)