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Chennai Mathematical Institute B.Sc. Entrance Exam
2019 CMI B.Sc. Entrance Exam
5
CMI Entrance #5
CMI Entrance #5
Source:
October 31, 2019
CMI
iterations
system of equations
geometric transformation
algebra
Problem Statement
Three positive reals
x
,
y
,
z
x , y , z
x
,
y
,
z
satisfy \\
x
2
+
y
2
=
3
2
y
2
+
y
z
+
z
2
=
4
2
x
2
+
3
x
z
+
z
2
=
5
2
.
x^2 + y^2 = 3^2 \\ y^2 + yz + z^2 = 4^2 \\ x^2 + \sqrt{3}xz + z^2 = 5^2 .
x
2
+
y
2
=
3
2
y
2
+
yz
+
z
2
=
4
2
x
2
+
3
x
z
+
z
2
=
5
2
.
\\ Find the value of
2
x
y
+
x
z
+
3
y
z
2xy + xz + \sqrt{3}yz
2
x
y
+
x
z
+
3
yz
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