Math Repository
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topic
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2017
P1 Q2
Topical
Equations
17 P1 Q2
2017 H2 Mathematics Paper 1 Question 2
Equations and Inequalities
Answers
(i)
(ii)
x
<
a
{x<a }
x
<
a
or
x
>
a
+
1
b
{x > a + \sqrt{\frac{1}{b}}}
x
>
a
+
b
1
Full solutions
(i)
(ii)
At intersection between the two graphs,
1
x
−
a
=
b
∣
x
−
a
∣
\frac{1}{x-a} = b\left|x-a\right|
x
−
a
1
=
b
∣
x
−
a
∣
Since
x
>
a
{x>a}
x
>
a
(from the graph),
1
x
−
a
=
b
(
x
−
a
)
b
(
x
−
a
)
2
=
1
(
x
−
a
)
2
=
1
b
\begin{gather*} \frac{1}{x-a} = b(x-a) \\ b (x-a)^2 = 1 \\ (x-a)^2 = \frac{1}{b} \\ \end{gather*}
x
−
a
1
=
b
(
x
−
a
)
b
(
x
−
a
)
2
=
1
(
x
−
a
)
2
=
b
1
Since
x
>
a
,
{x>a,}
x
>
a
,
x
=
a
+
1
b
x = a + \sqrt{\frac{1}{b}}
x
=
a
+
b
1
From the graphs, solution to
1
x
−
a
<
b
∣
x
−
a
∣
:
{\displaystyle \frac{1}{x-a} < b|x-a|: }
x
−
a
1
<
b
∣
x
−
a
∣
:
x
<
a
or
x
>
a
+
1
b
■
x<a \; \textrm{ or } \; x > a + \sqrt{\frac{1}{b}} \; \blacksquare
x
<
a
or
x
>
a
+
b
1
■
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