A Stumper

I was trying to solve this problem, but couldn't, even after an hour of toiling! Somebody from Brilliant, please help me!

(√2x-6) + (√x+4)= 5

#Jaysteller

Easy Math Editor

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Comments

X =5

Manu Attri - 7 years, 1 month ago

How? Can you work it out?

Jay Steller - 7 years, 1 month ago

What have you tried?

Try squaring the equation, what do you get? Does that get rid of the square roots?

Calvin Lin Staff - 7 years, 1 month ago

(√2x-6) + (√x+4)= 5
condition:x≥3 ==> [(√2x-6) + (√x+4)]²=5² <=> 2x-6 + 2(√2x-6)(√x+4) + x+4 = 25 <=> 3x-2 + 2(√2x²+2x-24) = 25 <=> 2(√2x²+2x-24) =27-3x ==>4(2x²+2x-24) = 27²-162x+9x² <=>x²-170x+825 = 0 <=>(x-5)(x-165) = 0 <=> x=5 or x=165 (satisfies) So, x=5 ; x=165

Jung Hyun Ran - 7 years, 1 month 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}`	$\boxed{123}$