Question

Question 7 of 10

Solve the rational equation:
2x² +1 + x = 3 + ²³1
3
2-1
O A. There is no solution.
B. x 1, x = 1
C. x = 1/3
O C.
D. X = 1
SUBMIT

Answer 1

To solve the rational equation 2x² + 1 + x = 3 + (23/31), subtract 3 from both sides and simplify the equation. Then, solve the resulting quadratic equation using the quadratic formula. The value of x is approximately 1.

Step-by-step explanation:

To solve the rational equation 2x² + 1 + x = 3 + (23/31), we need to simplify and solve for x. First, subtract 3 from both sides of the equation: 2x² + x - 2 = 23/31. Next, multiply both sides by 31 to clear the fraction: 62x² + 31x - 62 = 23. Rearranging the equation, we get 62x² + 31x - 85 = 0.

Now, we can solve this quadratic equation using factoring, completing the square, or the quadratic formula. In this case, factoring doesn't work, so we can use the quadratic formula: x = (-b ± sqrt(b² - 4ac)) / (2a). Plugging in the values a = 62, b = 31, and c = -85, we get the values of x as approximately -1.105 and 0.705. Therefore, the correct answer is D. x = 1.

Learn more about solving rational equations