SOLUTION: Find the set of all real solutions. If the solution set contains infinitely many elements, use interval notation to represent it.
{{{sqrt(2x+3)}}}-{{{sqrt(x-2)}}}=2
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-> SOLUTION: Find the set of all real solutions. If the solution set contains infinitely many elements, use interval notation to represent it.
{{{sqrt(2x+3)}}}-{{{sqrt(x-2)}}}=2
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Question 61754: Find the set of all real solutions. If the solution set contains infinitely many elements, use interval notation to represent it. -=2 Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! sqrt(2x+3)-{sqrt(x-2)=2
Square both sides to get:
(2x+3)-2sqrt(2x^2-x-6)+x-2=4
3x+1-2sqrt(2x^2-x-6)=4
2sqrt(2x^2-x-6)=3x-3
Square both sides to get:
4(2x^2-x-6)=9x^2-18x+9
8x^2-4x-24=9x^2-18x+9
x^2-14x+15=0
(x-15)(x+1)=0
x=15 or x=-1
Check these to see if they are extraneous.
Check x=15; OK as both neither integrand is negative.
Check x=-1; Extraneous as x-2 would be negative.
Only solution: x=15
Cheers,
Stan H.
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