An algebra problem

Given if x+y+z^(1/2)=670

x+y ^(1/2) +z=940

x^(1/2) +y+z=544

Find x+y+z My approach was that if i subtract first from second and third from second we get relation between the squares of thein sum with 1/2. But it got nowhere then. How can we approach it and prove that we have unique solutions to that?

#Algebra

Easy Math Editor

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Comments

Hint: Let $(x,y,z) = (X^2, Y^2, Z^2)$ .

Hint 2: Multiply all the equations by 4. Then apply completing the square.

Pi Han Goh - 3 years, 3 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$