X = the squareroot of the quantity of "a" minus the squareroot of the difference of "a" and "x". solve for x.

Question

Solve for x in terms of a. for a visual of the problem, the link is http://img259.imageshack.us/img259/8906/asdavg7.jpg . =| thanks. if you solve this problem, you're a genius! i heard that this problem could be solved by guessing for values of a and then finding a.. pattern? or by substituting a variable for the squareroot of a-x, but i dont know how to do it. anyway, thanks a bunch you guys.

Answer 1

You know the initial point for this problem.

1) Square both sides. This yields--

x^2 = a - sqrt (a+x)

2) Move the "a" to the other side to isolate the sqrt

x^2-a = sqrt (a+x)

3) Square both sides

(x^2-a)^2 = a+x

4) Move the a to the other side

(x^2-a)^2 - a = x

Now you've solved for x.

Of course, you could expand the left side exponent by using the FOIL method from algebra...

(x^4 - 2ax^2 + a^2) - a = x

However you want.

Good luck!

Mysstere

Answer 2

X = Sqrt { a - Sqrt ( a + x ) } get rid of the sqrt on the exterior bracket, sq. the two side X^2 = a - Sqrt ( a + x ) get rid of the sqrt on the bracket, sq. each and every sort. X^(2*2) = a^2 - ( a + x ) X^4 = a^2 - a - x X^4 + X = a^2 - a X ( X^3 + a million ) = a^2 - a X = ( a^2 - a ) / ( x^3 + a million ) answer?

Answer 3

X = Sqrt { a - Sqrt ( a + x ) }

get rid of the sqrt on the outside bracket, square both side

X^2 = a - Sqrt ( a + x )

get rid of the sqrt on the bracket, square each number.

X^(2*2) = a^2 - ( a + x )

X^4 = a^2 - a - x

X^4 + X = a^2 - a

X ( X^3 + 1 ) = a^2 - a

X = ( a^2 - a ) / ( x^3 + 1 ) answer?

Answer 4

If you break down the right side of the equation, you get:

x= the square root of a - the square root of a + x

Therefore, the two a's on the right cancle each other out, giving you:

x=x

Answer 5

x = (a - (a+x)^(1/2))^(1/2)
square both sides
(x)^2 = ((a - (a+x)^(1/2))^(1/2))^2
x^2 = a - (a+x)^(1/2) add (a+x)^(1/2) to both sides
(a+x)^(1/2) + x^2 = a sub x^2 from both sides
(a+x)^(1/2) = a - x^2
square both sides
((a+x)^(1/2))^2 = (a - x^2)^2
a + x = (a - x^2)^2
a + x = a^2 - 2ax^2 + x ^4
x^4 - 2ax^2 - x - a + a^2 = 0
x(x+1) = a-1 or x(x-1) = a