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2010 Saudi Arabia Pre-TST
3.4
2 parameter equation, 1/1(x + a)^2 - b^2} +...
2 parameter equation, 1/1(x + a)^2 - b^2} +...
Source: 2010 Saudi Arabia Pre-TST 3.4
December 28, 2021
parameterization
algebra
Problem Statement
Let
a
a
a
and
b
b
b
be real numbers such that
a
+
b
≠
0
a + b \ne 0
a
+
b
=
0
. Solve the equation
1
(
x
+
a
)
2
−
b
2
+
1
(
x
+
b
)
2
−
a
2
=
1
x
2
−
(
a
+
b
)
2
+
1
x
2
−
(
a
−
b
)
2
\frac{1}{(x + a)^2 - b^2} +\frac{1}{(x +b)^2 - a^2}=\frac{1}{x^2 -(a + b)^2}+\frac{1}{x^2-(a -b)^2}
(
x
+
a
)
2
−
b
2
1
+
(
x
+
b
)
2
−
a
2
1
=
x
2
−
(
a
+
b
)
2
1
+
x
2
−
(
a
−
b
)
2
1
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