![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 72 71" width="72"></svg>)
It is easy to find the solution of the equation x + 2 / x = 3 + 2 / 3 is X1 = 3, X2 = 2 / 3; the solution of X + 2 / x = 4 + 2 / 4 is X1 = 4, X2 = 2 / 4, x + 2 / x = 5 + 2 / 5 It is not difficult to find the solution of the equation x + 2 / x = 3 + 2 / 3 in the reading material, which is X1 = 3, X2 = 2 / 3; The solution of X + 2 / x = 4 + 2 / 4 is X1 = 4, X2 = 2 / 4 The solution of X + 2 / x = 5 + 2 / 5 is X1 = 5, X2 = 2 / 5 (1) Try to prove your conjecture by "finding the solution of the equation x + 2 / x = a + 2 / a about X"; (2) Using your conjecture, solve the equation x & sup2; - x + 2 / X-1 = a + 2 / A-1 about X
Conjecture: the solution of X + 2 / x = a + 2 / A is X1 = a, X2 = 2 / a.1) solve the equation x + 2 / x = a + 2 / A, get x ^ 2 - (a + 2 / a) x + 2 = 0 (x-a) (X-2 / a) = 0, X1 = a, X2 = 2 / A
X1 = - 2, X2 = 3 are the solutions of the equation (x + a) (X-B) = 0 to find a and B respectively
Cross multiplication
(x+2)(x-3)=0
So a = 2, B = 3
RELATED INFORMATIONS
- 1. Solving (3) x1-x2 with known equation x ^ 2-3x + 1 = 0
- 2. First read the following materials, and then answer the questions. Through observation, we find that the solution of the equation: x + 1 / x = 2 + 1 / 2 is X1 = 2, X2 = 1 / 2; X + 1 / x = 3 + 1 / 3 is X1 = 3, X2 = 1 / 3; X + 1 / x = 4 + 1 / 4 is X1 = 4, X2 = 1 / 4 Guess the solution of the equation X-1 / x = 1 and 1 / 2 about X and verify your conclusion
- 3. Given that X1 and X2 are the two real roots of the equation 4x ^ 2-4mx + m + 2 = 0, X1 ^ 2 + x2 ^ 2 = 4, find the value of M
- 4. The square of x minus 75 plus 2245 equals 0
- 5. Solution equation: (5x + 80) / (8x + 80) = 3 / 4
- 6. 30-2.5x = 10
- 7. The process of solving the equation exercise and the answer is 0.5 + 0.4 X
- 8. What does (1-1 / 2) x (1-1 / 3) x... X (1-1 / 19) x (1-1 / 20) equal fast
- 9. If 3x + 7 = 40, what is 9x + 21 So what's the sum of three eighths times 3x + 7 plus four eleventh
- 10. A number plus 40% of it is 7.8. To find this number, use the equation
- 11. Let the right focus of the ellipse x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 be f (C, 0) and a = 2C. Where are the two real roots of the equation AX ^ 2 + bx-c = 0 (x1, x2)
- 12. Let the eccentricity of the ellipse x2a2 + y2b2 = 1 (a > b > 0) be e, the right focus f (C, 0), and the two real roots of the equation AX2 + bx-c = 0 be X1 and X2 respectively, then the point P (x1, x2) () A. Must be in the circle x2 + y2 = 1 B. must be on the circle x2 + y2 = 1 C. must be outside the circle x2 + y2 = 1 D. the relation with x2 + y2 = 1 is related to E
- 13. (for a three digit number, the number on the hundreds is twice as big as the number on the tens, and the number on the one digit is twice as big as the number on the tens.) A three digit number in the hundreds is one times larger than the number in the tens, and the number in the one digit is one times smaller than the number in the tens. If the number in the hundred of the three digit number is exchanged with the number in the one digit number, then the three digit number is 99 times larger than the original three digit number, and the original three digit number can be obtained
- 14. There is a four digit number in the first day of math problem, which satisfies the following conditions: (1) the sum of two times of the number in one digit and two is less than half of the number in ten digit. (2) the number in ten digit There is a four digit number, which satisfies the following conditions: (1) the sum of two times and two is less than half of the ten digit number. (2) the number of one digit is transferred with the number of thousand digit, the number of ten digit is transferred with the number of hundred digit, and the new four digit number is the same as the original four digit number. (3) the sum of two digits and ten digit number is 10
- 15. Five times of a number minus one sixth of 120 is 35. What's the number
- 16. The basis for solving the equation, for example: subtraction equals subtraction of the subtracted
- 17. 40% of a number plus 3 equals 75% of 12. What's the number of ten
- 18. Given that a four digit number plus the sum of its digits is equal to 2008, then how much is the sum of all such four digits
- 19. X + (one and one third + one sixth) = 4.5,
- 20. What is five sixths minus one third