x 2 x 2 - c 2 = c 2 x 2 - c 2 + 39 In the given

Question

x 2 x 2 - c 2 = c 2 x 2 - c 2 + 39 In the given equation, c is a positive constant. Which of the following is one of the solutions to the given equation?

Accepted Answer

Choice D is correct. If x 2 - c 2 d 0 , then neither side of the given equation is defined and there can be no solution. Therefore, x 2 - c 2 > 0 . Subtracting c 2 x 2 - c 2 from both sides of the given equation yields x 2 x 2 - c 2 - c 2 x 2 - c 2 = 39 , or x 2 - c 2 x 2 - c 2 = 39 . Squaring both sides of this equation yields x 2 - c 2 x 2 - c 2 2 = 39 2 , or x 2 - c 2 x 2 - c 2 x 2 - c 2 = 39 2 . Since x 2 - c 2 is positive and, therefore, nonzero, the expression x 2 - c 2 x 2 - c 2 is defined and equivalent to 1 . It follows that the equation x 2 - c 2 x 2 - c 2 x 2 - c 2 = 39 2 can be rewritten as x 2 - c 2 x 2 - c 2 x 2 - c 2 = 39 2 , or 1 x 2 - c 2 = 39 2 , which is equivalent to x 2 - c 2 = 39 2 . Adding c 2 to both sides of this equation yields x 2 = c 2 + 39 2 . Taking the square root of both sides of this equation yields two solutions: x = c 2 + 39 2 and x = - c 2 + 39 2 . Therefore, of the given choices, - c 2 + 39 2 is one of the solutions to the given equation. Choice A is incorrect and may result from conceptual or calculation errors. Choice B is incorrect and may result from conceptual or calculation errors. Choice C is incorrect and may result from conceptual or calculation errors.

Question x-2-x-