Chapter 1 Quadratic Equations In One Unknown Worksheet With Answers Page 27
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341
Quadratic Equations in One Unknown
2.
Consider two positive odd numbers. Twice the product of the two numbers is larger than the
sum of the two numbers by 2. Find the smaller number.
Solution
Let x be the smaller number.
2 x ( x + 2) = x + ( x + 2) + 2
+ 4 x = 2 x + 4
2
2 x
+ 2 x − 4 = 0
2
2 x
+ x − 2 = 0
2
x
( x − 1)( x + 2) = 0
x = 1 or x = −2 (rejected)
∴ The smaller number is 1.
The length of AB and AC of a right-angled triangle are (x + 1) cm and
3.
C
(3x + 2) cm respectively. If the area of the triangle is 26 cm
2
, find AC.
Solution
(3 x + 2) cm
Q The area of the triangle is 26 cm
2
.
+
+
(
x
1 3
)(
x
2
)
∴
=
26
2
A
B
( x + 1) cm
+
+
=
2
3
x
5
x
2
52
+
−
=
2
3
x
5
x
50
0
−
+
=
(
3
x
10
)(
x
5
)
0
10
=
= −
x
or
x
5
(rejected)
3
10
+
∴ AC = 3
2
cm
3
= 12 cm
27
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