MindMap Gallery Equations and inequalities mind map
The properties of equations and inequalities are important concepts in high school mathematics. They have wide applications in algebra, functions, equations, and inequalities.
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This article discusses the Easter eggs and homages in Zootopia 2 that you may have discovered. The main content includes: character and archetype Easter eggs, cinematic universe crossover Easter eggs, animal ecology and behavior references, symbol and metaphor Easter eggs, social satire and brand allusions, and emotional storylines and sequel foreshadowing.
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Avatar 3 centers on the Sully family, showcasing the internal rift caused by the sacrifice of their eldest son, and their alliance with other tribes on Pandora against the external conflict of the Ashbringers, who adhere to the philosophy of fire and are allied with humans. It explores the grand themes of family, faith, and survival.
This article discusses the Easter eggs and homages in Zootopia 2 that you may have discovered. The main content includes: character and archetype Easter eggs, cinematic universe crossover Easter eggs, animal ecology and behavior references, symbol and metaphor Easter eggs, social satire and brand allusions, and emotional storylines and sequel foreshadowing.
[Zootopia Character Relationship Chart] The idealistic rabbit police officer Judy and the cynical fox conman Nick form a charmingly contrasting duo, rising from street hustlers to become Zootopia police officers!
Equality and Inequality
equation
Properties of equations and solution sets of equations
Properties of equations
If the same number or algebraic expression is added to both sides of the equation at the same time, the equality still holds
If both sides of the equation are multiplied by the same non-zero number or algebraic expression, the equation still holds.
Identity
Example: (a b)²=a² 2ab b²
solution set of equation
The set of all solutions to an equation is called the solution set of the equation
The solution set of a quadratic equation and the relationship between its roots and coefficients
Solution set of quadratic equation of one variable
When Δ>0
﹛[-b (b²-4ac)½]/2a, [-b- (b²-4ac)½]/2a﹜
When Δ=0
﹛-b/2a﹜
When Δ<0
Ø
The relationship between the roots and coefficients of a quadratic equation
Vedic theorem
x1 x2=-b/a
x1x2=c/a
inequality
Inequalities and their properties
If a>b, then a c>b c
If a>b,c>0 then ac>bc
If a>b,c<0 then ac<bc
If a>b,b>c then a>c
Transitivity
subtopic
subtopic
if a>b⇔b<a
symmetry
Compare size method
Make a errand
Comprehensive approach
Corollary 1 If a b>c then a>c-b
Corollary 2 If a>b,c>d, then a c>b d
Corollary 3 If a>b>0, c>d>0, then ac>bd
Corollary 4 If a>b>0, then a^n>b^n (n∈N, n>1)
Corollary 5 If a>b>0, then a½>b½
Proof method
Analysis
proof by contradiction
Solution sets of inequalities and solutions of groups of inequalities
The set of all solutions to an inequality is called the solution set of an inequality
For an inequality group obtained by combining several inequalities, the intersection of the solution sets of these inequalities is called the solution set of the inequality group.
Solution to Quadratic Inequality of One Variable
Quadratic inequality of one variable
The form is ax² bx c>0 (a, b, c, are constants and a≠0 where the inequality sign can also be <, ≤, ≥)
solution
It is most convenient to draw graphs with quadratic functions (factorization)
Mean inequality and its applications
If a and b are both positive numbers, then (a b)/2 ≥ (ab) ½
The equal sign holds true if and only if a=b