SOLUTION: Find all real number solutions of the equation algebraically: {{{ sqrt (2x+1) }}} - {{{ sqrt (x+1) }}} = 2 Can someone show me how to solve the problem by first isolating {

Algebra ->  Radicals -> SOLUTION: Find all real number solutions of the equation algebraically: {{{ sqrt (2x+1) }}} - {{{ sqrt (x+1) }}} = 2 Can someone show me how to solve the problem by first isolating {      Log On


   



Question 188921: Find all real number solutions of the equation algebraically:
+sqrt+%282x%2B1%29+ - +sqrt+%28x%2B1%29+ = 2

Can someone show me how to solve the problem by first isolating +sqrt+%282x%2B1%29+ on the left side of the equation and then squaring each side?

So the first step gives us...
+sqrt+%282x%2B1%29+ = 2+ +sqrt+%28x%2B1%29+

Now how do I square each side of this equation and find all solutions of x?

Found 2 solutions by ankor@dixie-net.com, Alan3354:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Find all real number solutions of the equation algebraically:
sqrt (2x+1) - sqrt (x+1) = 2
Can someone show me how to solve the problem by first isolating sqrt (2x+1) on the left side of the equation and then squaring each side?
So the first step gives us...
sqrt (2x+1) = 2+ sqrt (x+1)
:
Squaring both sides gives you 2x + 1 on the left but you have to FOIL the right side:
2x + 1 = 4 + 2sqrt(x+1) + 2sqrt(x+1) + (sqrt(x+1))^2
which is:
2x + 1 = 4 + 4sqrt(x+1) + x + 1
:
2x + 1 = 5 + x + 4sqrt(x+1)
Isolate the radical by itself on the right
2x - x + 1 - 5 = 4sqrt(x+1)
:
(x - 4) = 4sqrt(x+1)
:
Square both sides again, FOIL the left side
x^2 - 8x + 16 = 16(x+1)
:
x^2 - 8x + 16 = 16x + 16
:
x^2 - 8x - 16x + 16 - 16 = 0
:
x^2 - 24x = 0
Factor out x
x(x - 24) = 0
Two solutions
x = 0
and
x = +24, this is the only solution that works in the original equation
;
:
Did this help?

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
+sqrt+%282x%2B1%29+ - +sqrt+%28x%2B1%29+ = 2

Can someone show me how to solve the problem by first isolating +sqrt+%282x%2B1%29+ on the left side of the equation and then squaring each side?

So the first step gives us...
+sqrt+%282x%2B1%29+ = 2+ +sqrt+%28x%2B1%29+

Now how do I square each side of this equation and find all solutions of x?
-----------------
Square both sides
(2x+1) = 4 + 4sqrt(x+1) + (x+1)
Collect terms, isolate the sqrt
x = 4 + 4sqrt(x+1)
x-4 = 4sqrt(x+1)
Square again
x^2 - 8x + 16 = 16(x+1) = 16x + 16
x^2 - 24x = 0
x*(x-24) = 0
x = 0 (extraneous solution, ignore it)
x = 24