On the sum of two real number roots of X equation x & sup2; + 2 (K + 1) x + K & sup2; = 0 is m, and on the inequality system Y > - 4, y

On the sum of two real number roots of X equation x & sup2; + 2 (K + 1) x + K & sup2; = 0 is m, and on the inequality system Y > - 4, y

From - 4 = 0, k > = - 1 / 2
x1+x2=-2(k+1)=m>-4,kk>=-1/2

In what range does the equation kx2 + 2 (k-1) x - (k-1) = 0 have positive real roots?

When k = 0, the original equation is transformed to - 2x + 1 = 0, and the solution is x = 12. When k ≠ 0, ∵ △ 4 (k-1) 2 + 4K (k-1) = 8k2-8k + 4 = 8 (K-12) 2 + 2, ∵ △ 0, ∵ the equation has two unequal real roots. Let a and B be two, a + B = − 2 (k-1) k > 0, ab = k − 1K > 0, the value of ∵ K does not exist

Given that K is a nonnegative real number, the equation of X is: X & sup2; - (K + 1) x + k = 0 ①,kx²-（k+2）x+k=0…… ② When we find the value of K,
Given that K is a nonnegative real number, the equation of X is: X & # 178; - (K + 1) x + k = 0 ①,kx²-（k+2）x+k=0…… ② When finding the value of K, equation 1 and 2 have the same real root

Equation 1 (x-1) (x-k) = 0, x = 1, K
If the common root is x = 1, substitute it into equation 2, then k-k-2 + k = 0, then k = 2
If the common root is x = k, substitute it into equation 2 to get k ^ 3-K (K + 2) + k = 0, that is, K (k ^ 2-k-1) = 0 to get k = 0, (1 + √ 5) / 2, (1 - √ 5) / 2
Because K is nonnegative,
Three K values are obtained: 2,0, (1 + √ 5) / 2

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______ ．

Let the cross section be a, then the longitudinal intercept be 12-A, and the linear equation be XA + Y12 − a = 1. Substituting a (- 3, 4), we can get − 3A + 412 − a = 1. When a = - 4, a = 9, the linear equation is x9 + Y3 = 1. When a = - 4, we can get x + 3y-9 = 0. When a = - 4, we can get x − 4 + Y16 = 1, we can get y = 4x + 16

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______ ．

Let the transverse intercept be a, then the longitudinal intercept be 12-A, and the linear equation be XA + Y12 − a = 1. Substitute a (- 3, 4) to get − 3A + 412 − a = 1, and the solution be a = - 4, a = 9. When a = 9, the linear equation is x9 + Y3 = 1. When a = - 4, the linear equation is x − 4 + Y16 = 1, and the linear equation is y = 4x + 16. To sum up, the linear equation is x + 3y-9 = 0 or y = 4x + 16 6，．

If the line L passes through the point P (- 3,4) and the sum of the intercepts on the two coordinate axes is 12, then the general equation of the line
Senior high school sophomore math problem! ~ trouble will do it! ~ thank you

Let the equation be:
x/a+y/(12-a)=1
Because of (- 3,4)
therefore
-3/a+4/(12-a)=1
(A-9) (a + 4) = 0
A = 9 or - 4
So the equation is x / 9 + Y / 3 = 1 or - X / 4 + Y / 16 = 0
Then put it in the general form

If the line L passes through point a (1,2) and the intercept on two coordinate axes is equal, then the line equation satisfying the condition is______ ．

When the line L passes through the origin, its slope k = 2, then the linear equation is y = 2x; when the line L does not pass through the origin, let its equation be x + y = a, because point a (1,2) is on the line, so 1 + 2 = a, so a = 3, and the linear equation is y = - x + 3 or y = 2. So the answer is y = - x + 3 or y = 2

The equation of the line passing through point m (3, - 4) with equal intercept on the coordinate axis is______ ．

When the line passes through the origin, let the equation be y = KX, because the line passes through the point m (3, - 4), then - 4 = 3k, so k = - 43, then the linear equation is y = - 43x, that is 4x + 3Y = 0; when the line l does not pass through the origin, let the linear equation be x + y = a, then 3-4 = a, so a = - 1. The linear equation is x + y + 1 = 0, so the answer is 4x + 3Y = 0 or x + Y-1 = 0

Given that the line passes through the point (3,4), and the sum of the intercepts on the two coordinate axes is 2, the linear equation?

Let the intercept formula X / A + Y / b = 1, from the question a + B = 2, and then substitute (3,4) into the intercept formula, we can get the equations, then we can solve a and B

The equation of the line parallel to the line y = (- 3 / 4x) - 1 / 4 and the sum of the intercept on the two axes is 7 / 3 is

∵ parallel to the line y = (- 3 / 4x) - 1 / 4
Let the linear equation be y = (- 3 / 4x) + B
The intercept on the two axes is 4B / 3, B / 3 respectively
∵ the sum of intercepts on two axes is 7 / 3
∴4b/3+b=7/3
∴b=1
The linear equation is y = (- 3 / 4x) + 1