sqrt(x) = 1+a/x -- what is the solution?

Question

Hello,

How can I find the solution for this equation:

sqrt(x) = 1+a/x

if this equation has a name, whats is it called??

Thanks in advance for your help.

Answer 1

square both sides:
x = (1+a/x)^2
x = 1 +2a/x + a^2/x2
finding the common denominator:
x = x^2/x^2 +2ax/x^2 + a^2/x2
multiplying both sides by x^2
x^3 = x^2 + 2ax + a^2
The right side is a perfect square:
x^3 = (x+a)^2

I hope this helps

Answer 2

√x = 1 + a/x

Square both sides.
x = (1 + a/x)^2 = 1 + 2a/x + a^2/x^2

x - 1 - 2a/x - a^2/x^2 = 0
x^3 - x^2 - 2ax + a^2 = 0

Now it looks like a cubic equation.

Answer 3

Simplify:
(\/x)² = (1+a/x)²
x = [1² + 2a/x + (a/x)²]
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Answer 4

Are you sure you copied the problem correctly? We can only solve for one variable, either "x" or a..."