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CAN YOU HELP ME WITH A EQUATION? its the square root of 79 minus 5X equals X minus 11

Guest Mar 23, 2017
 #1
avatar+7085 
+1

one: \(\sqrt{79}-5x=x-11\)

  or

two: \(\sqrt{79-5x}=x-11\)          ?

hectictar  Mar 23, 2017
 #2
avatar+6979 
+1

I will solve both situations given by hectictar.

Situation 1:

\(\sqrt{79}-5x = x-11\\ 6x = \sqrt{79} + 11\\ x = \dfrac{\sqrt{79}+11}{6}\)


Situation 2:

\(\sqrt{79-5x}=x-11\\ 79-5x = x^2 -22x+121\\ x^2-17x+42=0\\ (x-14)(x-3) = 0\\ x = 14\text{ OR }3\)

MaxWong  Mar 23, 2017
 #3
avatar+7085 
+2

Hmmm, in situation 2, is x=3 really a solution?

 

I don't think it is, but I don't know what the " error " is in your work...

Is there a way to know that without just testing it in the end?

hectictar  Mar 26, 2017
 #4
avatar+6979 
+1

I know that!! But I am so careless......

If we substitute x = 3 into the original equation, we get sqrt(64) = 3 - 11 = -8. Since sqrt(64) = 8 not -8, so I should reject the solution x=3.

MaxWong  Mar 27, 2017

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