Given the equation x * - 5x - 1 = 0 about X, find the value of (1) x + 1 / X

Given the equation x * - 5x - 1 = 0 about X, find the value of (1) x + 1 / X

Given the equation x & sup2; - 5x - 1 = 0 about X, find the value of (1) x + 1 / X
Because x is not zero, divide both sides of the equation by X at the same time,
x-5-1/x=0,
X-1 / x = 5, squared, so,
x^2-2+1/x^2=25,
x^2+1/x^2=27,
x^2+2+1/x^2=29,
(x+1/x)^2=29
Because two X1 * x2 = - 1 > 0, X1 + x2 = 5,
So two, one positive and one negative
So x + 1 / x = ± √ 29

a^2+b^2
Known a + B = 5, ab = - 6. Find: A ^ 2 + B ^ 2 value. To write the process amount. Forget how to do, sweat

a+b=5
Square on both sides
a^2+2ab+b^2=25
ab=-6
So a ^ 2 + B ^ 2 = 25-2ab = 25-2 × (- 6) = 37

In the same plane rectangular coordinate system, if the intersection of the line y = 3x-1 and the line y = x-k is in the fourth quadrant, then the value range of K is ()
A. K ＜ 13b. 13 ＜ K ＜ 1C. K ＞ 1D. K ＞ 1 or K ＜ 13

The solution of the system of equations y = 3x − 1y = x − k about X and Y is: x = 1 − k2y = 1 − 3k2 ∵ the intersection point is in the fourth quadrant ∵ the system of inequalities 1 − K2 > 01 − 3k2 < 0 is obtained; the solution is 13 ∵ K < 1, so B is selected