To solve the equation with absolute value: given that x is a real number, M = | x + 1 | + | x + 2 | + | x + 3 |, find the minimum value of M
X = - 2
by
two
In general, f (x) = | x-a1 | + | x-a2 | +... + | x-an|
a1
RELATED INFORMATIONS
- 1. If the absolute value of the equation x + 1 plus the absolute value of X-1 about x equals that a has a real root, then the value range of the real number a is () A a is greater than or equal to 0 B A is greater than or equal to 0 C A is greater than or equal to 1 D A is greater than or equal to 2
- 2. If a is the real root of the equation x + log3x-3 = 0 and B is the real root of X + 3 ^ x-3, find a + B
- 3. The equation log3x ^ 2 + mlog1 / 3x ^ 2 + 5 = 0 of X has two equal real roots on (9, ∞), then the range of real number m is
- 4. The interval of a real root of equation x ^ 3-x-1 = 0 is
- 5. Let m be an integer and both of the equations 3x2 + mx-2 = 0 are greater than - 95 but less than 37, then M=______ .
- 6. Let m be an integer and both of the equations 3x2 + mx-2 = 0 are greater than - 95 but less than 37, then M=______ .
- 7. (1) Given that one root of the equation x & # 178; + 3x + M = 0 is twice the other root, find the value of M. (2) given the function y = MX & # 178; + 2 (M + 1) x + m, When m is a real number, the function image and X-axis: (1) have two different common points? (2) only one common point? (3) no common point? Please write the details,
- 8. If the two roots of equation 3x & # 178; + MX + n = 0 are 1, - 5 respectively, then M = n = necessary process
- 9. We know that the sum of two squares of the equation x2 + (M + 9) x + 2m + 6 = 0 is 24, then the value of M is equal to?
- 10. It is known that the sum of squares of X equation x & # 178; - 2 (M + 1) x + M & # 178; - 2 = 0 is equal to 8?
- 11. If there are exactly three different real solutions to the equation of X: the second power of X - 2 times the absolute value of X + 2 = m, please guess the value of M and verify it
- 12. If the absolute value of equation - X & # 178; + 4x-3 = KX has three real solutions, then K=
- 13. When the real number m takes what value, the equation 4x + (m-2) x + (m-5) = 0 has: (1) the absolute value of positive root is greater than that of negative root When m is a real number, the equations 4x + (m-2) x + (m-5) = 0 are as follows: (1) Is the absolute value of positive root greater than that of negative root? (2) Both are greater than 1?
- 14. 2,4 of 5,9 of 10,16 of 17, find the law
- 15. First simplify, then evaluate: - (square of X + square of Y) + [- 3xy - (square of X - square of Y)], where x = - 1, y = 2
- 16. First simplify and then evaluate: - (x2 + Y2) + [- 3xy - (x2-y2)], where x = - 1, y = 2
- 17. Simplification: - (square of X - square of Y) + [- 3xy - (square of X + square of Y)]: Xy - {the square of 1 / 2x - [the square of 3y-2 (the square of xy-3y) - 1]} If we know the square of a = 2A - 3AB, B = the square of a + 2Ab, we can find:
- 18. Calculate (3xy2-6x2y) / (- 2x) =___ .
- 19. Calculate (3xy2-6x2y) / (- 2x) =___ .
- 20. Simplification: (2x2y-3xy2) - (6x2y-3xy2)