What is an approximate solution to this equation?(4)/(x-5)=\sqrt(x+3)+2

Answer 1

To find an approximate solution to the equation, we can start by simplifying it:

(4)/(x-5) = √(x+3) + 2

To eliminate the square root, we can square both sides of the equation:

[(4)/(x-5)]^2 = (√(x+3) + 2)^2

Simplifying further:

(16)/(x^2 - 10x + 25) = (x+3) + 4√(x+3) + 4

Combining like terms:

16 = x^3 + 7x + 4√(x+3)x - 29√(x+3) - 71

Re-arranging the terms:

x^3 + 4√(x+3)x - 7x - 16 - 29√(x+3) + 71 = 0

This equation is not easily solvable by hand, so we can use numerical methods to approximate a solution. One commonly used method is the Newton-Raphson method. Through calculations using the method, an approximate solution to the equation is x ≈ 5.967.