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Find all values of x such that \sqrt{4x^2} + \sqrt{x^2} = 6 + 3x.

 Jul 10, 2023
 #1
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As you can see in the sqaure roots we can extract the x^2's, as \sqrt{x^2} = x, we can do the same with the 4 and our equation(s) become:

 

2x + x = 6 + 3x  (1)

-2x + x = 6 + 3x  (2)

2x - x = 6 + 3x  (3)

-2x - x = 6 + 3x  (4)

 

!! Notice the signs as (-2)^2 = (2)^2, and the prblem is asking us to find all values of x !!

 

Solving the equations we get that x=:

(1): x = no solution

(2): x = -3/2

(3): x = -3

(4): x = -1

 

So our answer is -3, -1, and -3/2! smiley

Hope this helped!

Other user, if you see a mistake please reply with your answer! I make mistakes!!

 

winkwinkwink

 Jul 12, 2023
 #2
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LouisBarger  Jul 12, 2023
edited by LouisBarger  Jul 20, 2023

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