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MATH / Find the largest positive real number λ such that for any nonnegative real numbers x, y, and z such that x²+y²+z²=1, the inequality λxy+yz≤(√(5))/(2)holds.

Problem

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problem

Find the largest positive real number λ\lambda such that for any nonnegative real numbers x,x, y,y, and zz such that x2+y2+z2=1,x^2 + y^2 + z^2 = 1, the inequality λxy+yz≤52\lambda xy + yz \le \frac{\sqrt{5}}{2}holds.
Plain-text mathematical notation (without MathML)
Find the largest positive real number λ such that for any nonnegative real numbers x, y, and z such that x²+y²+z²=1, the inequality
λxy+yz≤(√(5))/(2)holds.
Original LaTeX notation
Find the largest positive real number $\lambda$ such that for any nonnegative real numbers $x,$ $y,$ and $z$ such that $x^2 + y^2 + z^2 = 1,$ the inequality
\[\lambda xy + yz \le \frac{\sqrt{5}}{2}\]holds.

level

Level 4

type

Intermediate Algebra

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Source and history

task_id
cccc04ce-9f8e-5717-a638-8085270de870
task_key
intermediate~5falgebra--test--cccc04ce-9f8e-5717-a638-8085270de870
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import