Question

X+9=1/x+3 ..................

Answer 1

Наверно так........... ...

Answer 2

To solve the equation X + 9 = 1/X + 3, we'll need to simplify and manipulate the equation to isolate the variable X on one side. Here's how you can do it:

Step 1: Get rid of the fractions by multiplying every term by the common denominator, which in this case is X.

X * (X + 9) = 1 + 3X

Step 2: Expand the equation by distributing X to each term inside the parentheses.

X^2 + 9X = 1 + 3X

Step 3: Move all terms to one side to set the equation to zero.

X^2 + 9X - 3X - 1 = 0

Step 4: Combine like terms.

X^2 + 6X - 1 = 0

At this point, we have a quadratic equation. We can solve it by factoring, completing the square, or by using the quadratic formula. In this case, let's use the quadratic formula:

Step 5: Apply the quadratic formula: X = (-b ± √(b^2 - 4ac)) / (2a)

In our equation, a = 1, b = 6, and c = -1.

X = (-6 ± √(6^2 - 4 * 1 * -1)) / (2 * 1)

Simplifying further:

X = (-6 ± √(36 + 4)) / 2

X = (-6 ± √40) / 2

Step 6: Simplify the square root.

X = (-6 ± 2√10) / 2

Step 7: Simplify the expression by dividing both the numerator and denominator by 2.

X = -3 ± √10

Therefore, the solution to the equation X + 9 = 1/X + 3 is X = -3 + √10 or X = -3 - √10.