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Given that the sum of squares of the two equations x ^ 2 + (M + 9) x + 2m + 6 = 0 is 24, what is the value of M
Let two of the equations x ^ 2 + (M + 9) x + 2m + 6 = 0 be x1. According to Weida's theorem, X2 is: X1 + x2 = - (M + 9), x1x2 = 2m + 6 ∵ the sum of squares of the two is 24 ∵ X1 & # 178; + x2 & # 178; = 24 and X1 & # 178; + x2 & # 178; = (x1 + x2) &# 178; - 2x1x2 = (M + 9) &# 178; - 2 (2m + 6) ∵ (M + 9) &# 178; - 2 (2m + 6) = 24 ∵
RELATED INFORMATIONS
- 1. We know the equation x & # 178; - 2mx-2m-4 = 0 about X. when we prove the value of M, the sum of squares of the two equations is equal to 7
- 2. When m is the value, the intercept of the line (2M2 + M-3) x + (m2-m) y = 4m-1 on the X axis is 1
- 3. Given the line L: (m ^ 2-2m-3) x + (2m ^ 2 + m-1) y = 2m-1, the intercept on X axis and Y axis is equal, find the value of M
- 4. Let the linear l equation be x + my-2m + 6 = 0, and determine the value of m according to the following conditions (1) The intercept of L on the X axis is - 3; (2) The slope is 1
- 5. It is known that the equation of line L is x + my + 2m-1 = 0 (M is a parameter) (1) Verification: no matter what the value of M is, the straight line L passes through the fixed point; (2) If the intercept of the line L on the y-axis is - 5, find the analytic expression of L and the area of the figure enclosed by L and two coordinate axes
- 6. If a straight line passes through point a (- 3,4), and the sum of intercept on two axes is 12, then the linear equation is______ ．
- 7. The equation of a line passing through point m (3, - 4) with equal intercept on two coordinate axes
- 8. A straight line passes through the point m (- 3,4), and the sum of intercepts on the two coordinate axes is 12?
- 9. A straight line passes through the point m (2,1), and the sum of intercept on two coordinate axes is 6. The equation of the straight line is obtained
- 10. The equation of straight line passing through point m (3,4) with equal intercept on the coordinate axis is______ ．
- 11. 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?
- 12. 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?
- 13. If the two roots of equation 3x & # 178; + MX + n = 0 are 1, - 5 respectively, then M = n = necessary process
- 14. (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,
- 15. Let m be an integer and both of the equations 3x2 + mx-2 = 0 are greater than - 95 but less than 37, then M=______ ．
- 16. Let m be an integer and both of the equations 3x2 + mx-2 = 0 are greater than - 95 but less than 37, then M=______ ．
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- 18. 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
- 19. 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
- 20. 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