Given the function y = 2 / X and y = KX + 1, when k takes what value, the two function images always have a common point

Given the function y = 2 / X and y = KX + 1, when k takes what value, the two function images always have a common point

Y = 2 / X and y = KX + 1 have common solutions
2/x=kx+1
KX ^ 2 + X-2 = 0 has solution
1 + 8K is greater than or equal to 0, K is greater than or equal to - 1 / 8

Design an algorithm to calculate 1 * 3 * 5 * ······ 99 and draw the program diagram. What I want to ask is whether the initial variable I should be set to = 1 or 3?

It doesn't matter. 1 and 3 are OK

Design an algorithm to calculate 1 + 1 / 2 + 1 / 3 +... + 1 / 100
Design an algorithm to calculate 1 + 1 / 2 + 1 / 3 +... + 1 / 100
Please answer in Chinese

This is the best algorithm
(1+100)*100/2/100=(1+100)/2
Final output: (1 + 100) / 2.0
Remember to use 2.0, otherwise the result is not a decimal

The calculation method of 41 × 49 is as follows: 40 × 50 + 1 × 9
This is the fourth grade question, it's amazing! It's hard to imagine that the speed of knowledge infusion is so fast!

(40+1)*(50-1)
=40*50-40+50-1
=40*50+9*1

Given x ^ 3 + x ^ 2 + X + 1 = 0, find 1 + X + x ^ 2 + x ^ 3 + +The value of x ^ 2000. (P18 try)
Given x ^ 3 + x ^ 2 + X + 1 = 0, find 1 + X + x ^ 2 + x ^ 3 + +The value of x ^ 2000
Who answered well,
The correct answer is x ^ 2000
I am very grateful for your enthusiasm!
The answer is so wonderful, I really don't know who is the best
I have to leave it to other netizens to vote. Please forgive me

1+x+x^2+x^3+… +x^2000
=1+x+x^2+x^3+x^4(1+x+x^2+x^3)+x^8(1+x+x^2+x^3)… +x^1996(1+x+x^2+x^3)+x^2000
=x^2000
x^3+x^2+x+1=0
x^2(x+1)+(x+1)=0
(x^2+1)(x+1)=0
x=-1
The original formula is 1
Of course, it can be substituted directly. The number of 2001 is 1 and - 1 to offset, leaving 1
If you don't know the value of X, the answer is x ^ 2000

Given that X / (x ^ 2 + x-1) = 1 / 9, find the value of x ^ 2 / (x ^ 4 + x ^ 2 + 1)

A:
x/(x^2+x-1)=1/9
Reciprocal:
(x^2+x-1)/x=9
x+1-1/x=9
x-1/x=8
So:
The numerator and denominator of x ^ 2 / (x ^ 4 + x ^ 2 + 1) are divided by x ^ 2 to get:
=1/(x^2+1+1/x^2)
=1/[(x-1/x)^2+3]
=1/(8^2+3)
=1/67

Let x + 1 / x = 3 be known,
(1) X & sup2; + 1 / X & sup2;, (2) x & sup3; + 1 / X & sup3;, (3) x & sup2; + X & sup2; + 1

(1) X & sup2; + 1 / X & sup2; = x & sup2; + 2 + 1 / X & sup2; - 2 = (x + 1 / x) & sup2; - 2 = 3 & sup2; - 2 = 7, (2) x & sup3; + 1 / X & sup3; = (x + 1 / x) (X & sup2; - 1 + 1 / X & sup2;) = 3 × (7-1) = 18, (3) x & sup2 / / the fourth power of X + X & sup2; + 1 = 1 / (X & sup2; + 1 + 1 / X & sup2;) = 1 / (7 + 1

Given x ^ 2-2x-1 = 0, find the value of the algebraic formula x ^ 3-x ^ 2-3x + 2000

x^2-2x-1=0
∴x²-2x=1
x^3-x^2-3x+2000
=x(x²-2x)+x²-3x+2000
=x²+x-3x+2000
=x²-2x+2000
=1+2000
=2001

Given x + 1 / x = 2, x ^ 2 + 1 / x ^ 2 = 3, find the value of x ^ 3 + 1 / x ^ 3

x^3+1/x^3
=(x+1/x)(x^2-1+1/x^2)
=2×(3-1)
=4.

2x+x²=99

2x+x²=99
x²+2x+1=99+1
(x+1)²=100
x+1=±10
x1=9,x2=-11