Quadratic Equation - Turn Problem Sum to Solution Sum

Question

Pauline has two brothers, Peter and Philip. Pauline is x years old. Peter is 3 years older than Pauline. Philip is 2 years younger than Pauline.
a) Given that the product of the two brothers is 126 years, show that x^2 + x - 132 = 0.
b) Solve the equation to find the ages of the three children.


Strategies of solving Problem Sum

"Break into Pieces"

"Pauline is x years old" -> Pauline: x
"Peter is 3 years older than Pauline -> Peter: x + 3
NOTE: You just Link the Pauline's age to Peter's age, u will know Peter's actual age
You need to so-called rephrase English language to Maths Expression(Modification)

"Philip is 2 years younger than Pauline." -> Philip: x-2
NOTE: You need tobreak out into 3 sentences.
Understand sentence by sentence("Break Into Pieces").
Link one another if possible.

Transformation(Name to Algebra)
"...product of the two brother.." -> Peter * Philip
= (x+3) * (x-2) ; Tranformation:Name to Eqn
= x^2 - 2x + 3x - 6 ; Modification: Expansion
= x^2 + 3x - 2x - 6 ; Modification: Arrangement
= x^2 + x - 6 ; Combination: Comine 3x -2x to be x
NOTE: Form equation > Arrange x wif x, No. wif No. > Combine: 2x + 1

"...is 126." -> x^2 + x - 6 = 126

Modification using the Power of BALANCE: x^2 + x - 6 - 126 = 126 - 126
x^2 + x - 132 = 0 (shown)

"Solve..." means to find unknown x

Since it is Qudratic Eqn, therefore you should use General Formula
(See How powerful "Question is the Answer")

------------------- ----------------- SUMMARY ------------------------------------------
1. Question is the Answer - you don't need to memorize. Just SEE and Do it!
2. Break Into Pieces - for clearer interpret, therefore better understanding
3. Transformation - Sentence to a 'Picture' form for anlayzing clearly
4. Modification - do a powerful presentation
5. Combination - combine whatever info you have understand after 'break into pieces'
6. Linking - Link up all present info that you have just combined and bring your PAST
(what you have learnt) to link to the present information!
------------------------------------- SUMMARY -------------------------------------------

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