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Formulae of Algebra II
08.11.2012, 8:04:09 PM

Algebra

 Word Excel
 ℕ ⊂ ℤ ⊂ ℚ ⊂ ℝ
 natural()=subset(integer())=subset(rational())=subset(real())

 △ABC, a⊥h, p=P÷2:

S=ah/2=0.5ah=√p͞(͞p͞−͞a͞)͞(͞p͞−͞b͞)͞(͞p͞−͞c͞)

 triangle(ABC), a=perpend(h), p=P/2:

S=ah/2=0.5ah=sqrt(p(p-a)(p-b)(p-c))
 √x̅=a, a²=x sqrt(x)=a, a^2=x
 √−͞x=ai, x>0 sqrt(-x)=ai, x>0
 −√x̅=−a, x>0 -sqrt(x)=-a, x>0
 ABC, ∠C=90°, AB=c, BC=a, AC=b:

a²+b²=c²

 triangle(ABC), angle(C)=90*degree(), AB=c, BC=a, AC=b:

a^2+b^2=c^2

 √x͞y=√x̅×√y̅  sqrt(xy)=sqrt(x)*sqrt(y)
 √x͞/͞y=√x̅/√y̅  sqrt(x/y)=sqrt(x)/sqrt(y)
 √x͞²=|x|  sqrt(x^2)=|x|

 CLASSIC QUADRATIC EQUATION:

ax²+bx+c=0

D=b²−4ac

x=(−b±√D̅)/2a

THEOREM OF VIETA: x₁+x₂=−b/a, x₁x₂=c/a

 CLASSIC QUADRATIC EQUATION:

ax^2+bx+c=0

D=b^2-4ac

x=(-b(+-)sqrt(D))/2a

THEOREM OF VIETA: x(1)+x(2)=-b/a, x(1)x(2)=c/a

 REDUCED QUADRATIC EQUATION:

x²+px+q=0

D=p²−4q

x=(−p±√D̅)÷2

THEOREM OF VIETA: x₁+x₂=−p, x₁x₂=q

 REDUCED QUADRATIC EQUATION:

x^2+px+q=0

D=p^2-4q

x=(-p(+-)sqrt(D))/2

THEOREM OF VIETA: x(1)+x(2)=-p, x(1)x(2)=q

 √a͞±͞√͞b̅=√(a͞+͞√͞(͞a͞²͞−͞b͞)͞/͞2±√a͞−͞√͞(͞a͞²͞−͞b͞)͞/͞2 sqrt(a(+-)sqrt(b))=sqrt((a+sqrt(a^2-b))/2)(+-)sqrt((a-sqrt(a^2-b))/2)
 Pₙ=n! P(n)=n!

 △ABC WITH BISECTOR AD:

BD/CD=AB/AC

 triangle(ABC) WITH BISECTOR AD:

BD/CD=AB/AC

 △ABC∼△ABC:

∠A=∠A₁, ∠B=∠B₁, ∠C=∠C

AB/A₁B₁=BC/B₁C₁=AC/A₁C₁=k

S/S₁=k²

 triangle(ABC)=similar(triangle(A(1)B(1)C(1))):

angle(A)=angle(A(1)), angle(B)=angle(B(1)), angle(C)=angle(C(1))

AB/A(1)B(1)=BC/B(1)C(1)=AC/A(1)C(1)=k

S/S(1)=k^2

Category: My files | Added by: Elektronika_XQ-19 | Tags: algebra, math
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