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avatar+921 

Solve for x.

√x+5= √x+ 1

 

no solution

 

4

 

−4

 

2

 

I think it would be 4? I am not sure.

 Oct 24, 2018

Best Answer 

 #3
avatar
+2

Solve for x:
sqrt(x + 5) = sqrt(x) + 1

Raise both sides to the power of two:
x + 5 = (sqrt(x) + 1)^2

Subtract (sqrt(x) + 1)^2 from both sides:
5 - (sqrt(x) + 1)^2 + x = 0

5 - (sqrt(x) + 1)^2 + x = 4 - 2 sqrt(x):
4 - 2 sqrt(x) = 0

Subtract 4 from both sides:
-2 sqrt(x) = -4

Divide both sides by -2:
sqrt(x) = 2

Raise both sides to the power of two:
x = 4

 Oct 24, 2018
 #1
avatar+101234 
+1

As you have it written....no  solution

 

Think about this....whatever √ x  is on one side it is the same thing on the other side

 

But  adding 5 to this value on one side will always be  3 more than adding 2 to it on the other side

 

So.... the left side > right side for any  x value  ≥ 0

 

 

cool cool cool

 Oct 24, 2018
 #2
avatar+921 
0

This is how it looks would it still be no soultion ? i am kinda confused.

 

the square root goes only goes across x+5 and the square root just goes on x for the second equation

jjennylove  Oct 24, 2018
edited by jjennylove  Oct 24, 2018
 #3
avatar
+2
Best Answer

Solve for x:
sqrt(x + 5) = sqrt(x) + 1

Raise both sides to the power of two:
x + 5 = (sqrt(x) + 1)^2

Subtract (sqrt(x) + 1)^2 from both sides:
5 - (sqrt(x) + 1)^2 + x = 0

5 - (sqrt(x) + 1)^2 + x = 4 - 2 sqrt(x):
4 - 2 sqrt(x) = 0

Subtract 4 from both sides:
-2 sqrt(x) = -4

Divide both sides by -2:
sqrt(x) = 2

Raise both sides to the power of two:
x = 4

Guest Oct 24, 2018

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