- #1

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- 0

## Homework Statement

Prove that √x+y ≤ √x + √y for all x,y ≥ 0

## Homework Equations

## The Attempt at a Solution

square both sides: x + y ≤ x + 2√x√y + y

subtracting x and y: 0 ≤ 2√x√y

dividing by 2: 0 ≤ √x√y

0 ≤ √x√y is true for all x,y since the square root of a number is always non negative, and two non negatives multiplied together gives you a non negative number.

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I submitted this proof and got 2/10 on it, but I have no clue where I went wrong. Am I missing something obvious?