If $$6-\frac{9}{x}=x$$ then x has how many possible values? (A) None (B) One (C) Two (D) A finite number greater than two (E) Three The OA is B. Can anye expert explain this PS question please? Thanks.

6-9/x = x When x=1 --> 6-9 = -3 When x=2 --> 6-4.5 = 1.5 When x=3 --> 6-3 = 3 When x=4 --> 6-9/4 not equal to 4 and same is the case for any other value for x henceforth So x has only one possible value 3. Other way to solve: Algebrically, this will be of form (x-a)(x-b) = x$$^2$$ -ax -bx +ab From the question, ab = 9. Since 3*3 = 9. a=b=3. Hence the solution is (x-3)$$^2$$ and x value will be 3 --> only one possible value.

LUANDATO wrote:If $$6-\frac{9}{x}=x$$ then x has how many possible values? (A) None (B) One (C) Two (D) A finite number greater than two (E) Three Multiplying both sides by x, we get: 6x - 9 = x² 0 = x² - 6x + 9 0 = (x-3)(x-3). Thus, x=3. The correct answer is B.

If $$6-\frac{9}{x}=x$$ then x has how many possible values? (A) None (B) One (C) Two (D) A finite number greater than two (E) Three Hi LUANDATO, Let's take a look at your question. $$6-\frac{9}{x}=x$$ $$6=x+\frac{9}{x}$$ Simplify right hand side by adding up like terms. $$6=\frac{x^2+9}{x}$$ $$6x=x^2+9$$ $$x^2-6x+9=0$$ Let's factorize the left hand side by grouping, $$x^2-3x-3x+9=0$$ $$x(x-3)-3(x-3)=0$$ $$(x-3)(x-3)=0$$ $$Either (x-3)=0 or (x-3)=0$$ It gives us: $$x = 3$$ It means x has only one value. Therefore, Option B is correct. Hope this helps. I am available if you'd like any follow up.

BTGmoderatorLU wrote:If $$6-\frac{9}{x}=x$$ then x has how many possible values? (A) None (B) One (C) Two (D) A finite number greater than two (E) Three The OA is B. Can anye expert explain this PS question please? Thanks. Multiplying the given equation by x, we have: 6x - 9 = x^2 x^2 - 6x + 9 = 0 (x - 3)(x - 3) = 0 x = 3 Answer: B

BTGmoderatorLU wrote:If $$6-\frac{9}{x}=x$$ then x has how many possible values? (A) None (B) One (C) Two (D) A finite number greater than two (E) Three Given: 6 - 9/x = x Multiply both sides of the equation by x to get: 6x - 9 = x² Rearrange to get: x² - 6x + 9 = 0 Factor to get: (x - 3) (x - 3) = 0 So, x = 3 (one solution) Answer: B Cheers, Brent

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