SOLUTION: {{{sqrt(4x+1)-sqrt(2x+4)=1}}}

Algebra ->  Radicals -> SOLUTION: {{{sqrt(4x+1)-sqrt(2x+4)=1}}}      Log On


   

Question 904562: sqrt%284x%2B1%29-sqrt%282x%2B4%29=1
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%284x%2B1%29-sqrt%282x%2B4%29=1

add sqrt%282x%2B4%29 to both sides of the equation to get:

sqrt%284x%2B1%29 = sqrt%282x%2B4%29%2B1

square both sides of the eqaution to get:

4x%2B1 = 2x+%2B+4+%2B+2%2Asqrt%282x%2B4%29+%2B+1

combine like terms to get:

4x%2B1 = 2x+%2B+5+%2B+2%2Asqrt%282x%2B4%29

subtract 2x and subtract 5 from both sides of the equation to get:

4x+%2B+1+-+2x+-+5 = 2+%2A+sqrt%282x%2B4%29

simplify to get:

2x+-+4 = 2+%2A+sqrt%282x+%2B+4%29

divide both sides of the equation by 2 to get:

x+-+2 = sqrt%282x%2B4%29

square both sides of the equation to get:

%28x-2%29%5E2 = %282x%2B4%29

simplify to get:

x%5E2+-+4x+%2B+4 = 2x+%2B+4

subtract 2x and subtract 4 from both sides of the equation to get:

x%5E2+-+6x = 0

complete the squares to get:

x-3%29%5E2+-+9 = 0

add 9 to both sides of the equation to get:

x-3%29%5E2 = 9

take the square root of both sides of the equation to get:

x-3 = +/- 3

add 3 to both sides of the equation to get:

x = 3+%2B+3 or x = 3+-+3

that makes x = 6 or x = 0

when x = 6, the original equation becomes sqrt%2825%29+-+sqrt%2816%29+=+1 which becomes 5+-+4+=+1 which is true because 1 = 1.

when x = 0, the original equation becomes sqrt%281%29+-+sqrt%284%29+=+1 which becomes 1+-+2+=+1 which is false because -1 does not equal 1.

your solution is therefore that x = 6.








Answer by MathTherapy(10719) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%284x%2B1%29-sqrt%282x%2B4%29=1
*****************************
It is UNBELIEVABLE that the person who responded to this problem applied this RIDICULOUS approach. 

The person got up to x%5E2+-+6x+=+0, and UNBELIEVABLY, HE chose to, "complete the squares........"
What would behoove someone to suggest such a thing to a person who asks for help with a math problem?
Now, isn't x%5E2+-+6x+=+0 SIMPLY x(x - 6) = 0, which results in values of 0 and 6 for x? Why would someone
go through all that trouble to COMPLETE the SQUARE here? It's the same as using the quadratic equation formula
to solve it, which is EXTREMELY RIDICULOUS and TOTALLY UNNECESSARY.....a TOTAL waste of time, in this author's
opinion. Some people are probably more eccentric than is realized!!