Formulas for Problem Solving

Key Questions

  • What are commonly used formulas used in problem solving?

    Answer:

    A few examples...

    Explanation:

    I will assume that you mean things like common identities and the quadratic formula. Here are just a few:

    Difference of squares identity

    #a^2-b^2 = (a-b)(a+b)#

    Deceptively simple, but massively useful.

    For example:

    #a^4+b^4 = (a^2+b^2)^2 - 2a^2b^2#

    #color(white)(a^4+b^4) = (a^2+b^2)^2 - (sqrt(2)ab)^2#

    #color(white)(a^4+b^4) = ((a^2+b^2) - sqrt(2)ab)((a^2+b^2) +sqrt(2)ab)#

    #color(white)(a^4+b^4) = (a^2-sqrt(2)ab+b^2)(a^2+sqrt(2)ab+b^2)#

    Difference of cubes identity

    #a^3-b^3 = (a-b)(a^2+ab+b^2)#

    Sum of cubes identity

    #a^3+b^3 = (a+b)(a^2-ab+b^2)#

    Quadratic formula

    Very useful to know, better if you know how to derive it:

    The zeros of #ax^2+bx+c# are given by:

    #x = (-b+-sqrt(b^2-4ac))/(2a)#

    Pythagoras theorem

    If a right angled triangle has legs of length #a, b# and hypotenuse of length #c# then:

    #c^2 = a^2+b^2#

    This is also very useful in trigonometric form. If we have an angle #theta# in a right-angled triangle, then we call the side nearest #theta#, the #"adjacent"# side, the side opposite it the #"opposite"# side and the hypotenuse the #"hypotenuse"#.

    Then:

    #"hypotenuse"^2 = "adjacent"^2 + "opposite"^2#

    Dividing both sides by #"hypotenuse"^2#, we get:

    #1 = ("adjacent"/"hypotenuse")^2 + ("opposite"/"hypotenuse")^2#

    That is:

    #1 = cos^2 theta + sin^2 theta#

    Then dividing both sides by #cos^2 theta# we find:

    #sec^2 theta = 1 + tan^2 theta#

    Binomial theorem

    #(a+b)^n = sum_(k=0)^n ((n), (k)) a^(n-k) b^k#

    where #((n), (k)) = (n!)/((n-k)! k!)#

    For example:

    #(x+1)^4 = x^4+4x^3+6x^2+4x+1#

    George C. · 2 · Feb 10 2018
  • How do you know which formulas to use when solving a word problem?

    Hmmm, there is no rule when you have a word math problem and also there is no specific forumula that you use when you need to solve word problem. It is all about logic. If you want, you can post question (specific word problem) and we will anwer it and explain how to solve it.

    Deevona · 1 · Dec 16 2014
  • How do you solve word problems involving formulas?

    Answer:

    By reading.

    Explanation:

    The way you interpret the problem is the start, let me give you an example:

    Triangle "1" Has 3 sides, #A#, #B#, and #C#. #A# Is equal to #3#, #B# is equal to #4#. Find #C#.

    Using Pythagoras' Theorem, we know #A^2 + B^2 = C^2#

    #A^2 = 9#, #B^2 = 16 implies A^2 + B^2 = 9 + 16 = 25#

    SInce #C^2 = A^2 + B^2 = 25#, you know that

    #C = sqrt(C^2) = sqrt(25) = 5#

    You simply find out what value goes with what part of the formula, and do this for each, and then work out the formula as normal.

    Pythagoras · 2 · Sep 20 2015

Questions

Linear Equations