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Find all nonnegative numbers x such that \(\sqrt{x}+2=\sqrt{x+100}.\)

 Oct 16, 2019

Best Answer 

 #3
avatar
+2

Solve for x:
sqrt(x) + 2 = sqrt(x + 100)

Raise both sides to the power of 2:
(sqrt(x) + 2)^2 = x + 100

Subtract x + 100 from both sides:
-100 + (sqrt(x) + 2)^2 - x = 0

-100 + (sqrt(x) + 2)^2 - x = 4 sqrt(x) - 96:
4 sqrt(x) - 96 = 0

Add 96 to both sides:
4 sqrt(x) = 96

Divide both sides by 4:
sqrt(x) = 24

Raise both sides to the power of two:
 
 x = 576

 Oct 16, 2019
 #1
avatar
+2

I could find only one positive value for x:

 

x = 576

 Oct 16, 2019
 #2
avatar+969 
+2

I graphed the equations and found that the only value is x = 576

 Oct 16, 2019
 #3
avatar
+2
Best Answer

Solve for x:
sqrt(x) + 2 = sqrt(x + 100)

Raise both sides to the power of 2:
(sqrt(x) + 2)^2 = x + 100

Subtract x + 100 from both sides:
-100 + (sqrt(x) + 2)^2 - x = 0

-100 + (sqrt(x) + 2)^2 - x = 4 sqrt(x) - 96:
4 sqrt(x) - 96 = 0

Add 96 to both sides:
4 sqrt(x) = 96

Divide both sides by 4:
sqrt(x) = 24

Raise both sides to the power of two:
 
 x = 576

Guest Oct 16, 2019

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