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ISI B.Math Entrance Exam
2008 ISI B.Math Entrance Exam
8
B.Math 2008-Equations
B.Math 2008-Equations
Source: 10+2
April 16, 2012
quadratics
trigonometry
algebra proposed
algebra
Problem Statement
Let
a
2
+
b
2
=
1
a^2+b^2=1
a
2
+
b
2
=
1
,
c
2
+
d
2
=
1
c^2+d^2=1
c
2
+
d
2
=
1
,
a
c
+
b
d
=
0
ac+bd=0
a
c
+
b
d
=
0
Prove that
a
2
+
c
2
=
1
a^2+c^2=1
a
2
+
c
2
=
1
,
b
2
+
d
2
=
1
b^2+d^2=1
b
2
+
d
2
=
1
,
a
b
+
c
d
=
0
ab+cd=0
ab
+
c
d
=
0
.
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