If the equation x3-x-1 = 0 has a root on the interval (a, b) (a ∈ Z., B ∈ z) of length 1, then a + B =?
Let f (x) = x ^ 3-x-1, then f '(x) = 3 * x ^ 2-1, f' (x) = 6x
Let f '(x) = 0, then x = ± (radical 3) / 3;
When x = (radical 3) / 3, f '((radical 3) / 3) > 0, then f (x) has a minimum value = - 2 (radical 3) / 9 - 1
RELATED INFORMATIONS
- 1. If the equation x3-6x + 5-a = 0 about X has three different real roots, find the value range of A
- 2. If the absolute value x + a = 0 of the equation x2-2 of X has four different real roots, find a zero point of the range function X3 + x-3 of A
- 3. It is proved that the equation (the 5th power of x) - 5x + 1 = 0 has and only has one positive real root less than 1 Proof equation (the 5th power of x) - 5x + 1 = 0 has only one positive real root less than 1 At present, we are learning differential mean value theorem, hope the method is related to this. Thank you!
- 4. It is proved that the quintic power + 5x-4 = 0 of equation x has and has only one real root
- 5. It is proved that the equation x ^ 5 + 5x + 1 = 0 has and only has one real root in the interval (- 1,0)
- 6. The number of real roots of equation X3 + 6x2 + 9x + 4 = 0 is () and the answer is 2 x followed by several powers -3 and - 1 do wrong friends, please look through the problem, this is the derivative part of the process, let its derivative = 0, and then find - 1, - 3 did not understand what the real root refers to
- 7. Proof: the equation X3 + 2x-3 = 0 has only one real root of 1 X3 is the third power of X
- 8. When a takes what value, the equation x3-3x2-a = 0 has exactly one real root, two unequal real roots and three unequal real roots?
- 9. The equation x3-3x-m = 0 has real roots on [0,1], and the maximum value of M is obtained
- 10. The equation x3-3x2 + 3x = 0 has several real roots?
- 11. It is known that the equation x3-ax2-2ax + A2-1 = 0 about X has and only has one real root. Find the value range of real number a
- 12. If the equation x3-x + 1 = 0 has exactly one zero point in the interval (a, b) (a, B are integers and B-A = 1), then a + B=______ .
- 13. It is proved that no matter what the value of B is, the equation x ^ 3-3x ^ 2 + B = 0 has at most one real root in the interval [0,1]
- 14. It is proved that the equation x ^ 3-3x + 1 = 0 can not have two different roots on the interval [0,1]?
- 15. It is proved that the equation x & sup3; - 3x + 1 = 0 cannot have two different roots on the interval [0,1]
- 16. It is proved that the equation x = asinx + B (a > 0, b > 0) has at least one positive root not exceeding a + B
- 17. It is proved that the equation x = asinx + B, where a > 0, b > 0, has at least one positive root, and it does not exceed a + B
- 18. It is proved that the equation x = asinx + B, where a > 0 and b > 0 have at least one positive root and it does not exceed a + B
- 19. It is proved that the equation x = asinx + B (a > 0, b > 0) has at least one positive root not greater than B + a
- 20. It is proved that the equation x ^ 5 + X + 1 = 0 has only one real root in the interval (- 1,0)