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:
- = 2
Can someone show me how to solve the problem by first isolating on the left side of the equation and then squaring each side?
So the first step gives us... = 2+
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) (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?
Can someone show me how to solve the problem by first isolating on the left side of the equation and then squaring each side?
So the first step gives us... = 2+
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
