Page 83 - Mathematics_Form_Two

Algebra

Example 4�35 Taking square root on both sides gives
5 5 81
2
What must be added to x − x to make x + 2 = ± 4
it a perfect square? 2

Solution x + 5 = ± 9
5x + FOR ONLINE READING ONLY
2
2
5
–
The coefficient of x is − . 5 9
2 Thus, x = − .
5 1 5 æ 5 ö 2 2
Half of - is ç - ÷ = - . 5 9
5
2 2 2 è 4 ø Either x x = - + or x = -- 9 . Mathematics for Secondary Schools
2 2 2 2
 5 5  2 25 Thus, x = or x = - 7.
2
−
The square of −  is = .

 4 4  16 Therefore, x = or x = - 7.
2
2
Therefore, 25 must be added to x − 5 x
16 2
to make it a perfect square. Example 4�37
Example 4�36 Solve the quadratic equation
2
20
x − 5x += by completing the
Solve the quadratic equation x + 2 5x − 14 0= square.
by completing the square.
Solution
Solution
20
2
Given x − 5x += . It follows that
The equation x + 2 5x − 14 0= has to be 2
rearranged so that the left-hand side is x − 5x = − 2
converted to a perfect square. x − 5x + 25 = −+ 25
2
2
From x + 2 5x − 14 0= . It follows that 4 4
2 8 25
x + 2 5x = 14 æ ç x - 5 ö ÷ = - +
Add the square of half the coefficient of x è 2 4 ø
on both sides to get,   x − 5   2 = 17

25 25  2  4
x + 2 = 14 +
4 4 5 5 5 17 17
17
x − x − ± == x =
Factorize the LHS to obtain, 2 2 2 4 4 4
+
 5  2 56 25 x = 5 ± 17
 x +  = 2 4
 2  4
 5  2 81 5 17
 x +  = x = ±
 2  4 2 2

77
Student's Book Form Two

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MATHEMATIC F2 v5.indd 77 11/10/2024 20:12:02
MATHEMATIC F2 v5.indd 77