Page 27 - DMTH202_BASIC_MATHEMATICS_II

Basic Mathematics-II

Notes 2.2.3 Method 3: Evaluate and Solve Equations

Assess both sides of equation (*) at r points where r is the number of unidentified coefficients.
Setting the sides equal at these points provide k linear equations for these unknowns.
Solve them. (Suitable points to select are usually 0,1,–1, or near infinity.)

Example: of method 3

5
Considering that a = –17; a = 44, assess both sides near infinity. The left side appears as , the
10 20 x
44 a 12

right side appears as ; conclude a = – 39.
x 12
To verify, assess at some other point and ensure the sides are equivalent there.
set x = 0;

 7
LHS 
 12
7

12
 17 39 44
RHS   
4  2  3

 51 234 176 7

 
12 12
2.2.4 Method 4: Common Denominator

Write both sides of (*) as polynomials aided by Q(x).
The coefficients in these polynomials of every power of x must consent; these provide linear
equations for the unknown. Solve them.

Example: of method 4
Find
2
7

5x  2x   a (x  3) a (x  2)(x  3) a (x  2) 2

10 11 20
Deduce
5  a  a
11 20
2  a  5a  4a 20
10
11
 7   3a  6a  4a 20
10
11
Solve these equations.

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