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

"According to the meaning of the title, we get X1 + x2 = 4m / 4 = MX1 * x2 = (M + 2) / 4x1 ^ 2 + x2 ^ 2 = 4x1 ^ 2 + x2 ^ 2 + 2x1 * x2-2x1 * x2 = 4 (x1 + x2) &# 178; - 2x1 * x2 = 4m & # 178; - (M + 2) / 2 = 42m & # 178; - m-2 = 82m & # 178; - M-10 = 0 (2m-5) (M + 2) = 0m = 5 / 2 or M = - 2

It is known that X1 and X2 are two real roots of the equation 4x ^ 2-4mx + m + 2 = o
1. When m is a real number, X1 ^ 2 + x2 ^ 2 get the minimum value
2. If X1 and X2 are greater than 1 / 2, find the value range of M

According to Vader's theorem, X1 + x2 = - B / a = - (- 4m) / 4 = MX1 + x2 = C / a = (M + 2) / 4 (1) X1 ^ 2 + x2 ^ 2 = (x1 + x2) & sup2; - 2x1x2 = M & sup2; - 2 * (M + 2) / 4 = M & sup2; - M / 2-1 = (m-1 / 4) & sup2; - 1-1 / 16 = (m-1 / 4) & sup2; - 17 / 16 when m = 1 / 4, X1 ^ 2 + x2 ^ 2 has the minimum value

The difference between three times of a number and one-half of this number is more than two-thirds of this number. How much is this number? Solving the equation requires listing the equation process

Let this number be X
It's three times 3x
One half of this number is x / 2
The difference between three times of a number and one half of the number is 3x-x / 2
Two thirds of this number is 2x / 3
The difference between three times of a number and one-half of the number is five times more than two-thirds of the number
by
3X-X/2 - 2X/3=5
3X-3X/6-4X/6=5
3X-7X/6=5
(18X-7X)/6=5
11X=30
X=30/11

What is the sum of two-thirds, one-half, one seventh of a number and itself is 37

X + two thirds x + one half x + one seventh x = 37

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