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Algebra and Applications Test 3
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© examsnet.com
Question : 2
Total: 25
If
x
=
√
3
−
√
2
√
3
+
√
2
and
y
=
√
3
+
√
2
√
3
−
√
2
, then the value of
x
3
+
y
3
is:
730
650
970
950
Validate
Solution:
x
=
√
3
−
√
2
√
3
+
√
2
=
√
3
−
√
2
√
3
+
√
2
×
√
3
+
√
2
√
3
−
√
2
=
5
−
2
√
6
Similarly,
y
=
√
3
+
√
2
√
3
−
√
2
=
5
+
2
√
6
Now,
x
3
+
y
3
=
(
5
−
2
√
6
)
3
(
5
+
2
√
6
)
3
=
125
−
48
√
6
−
30
√
6
(
5
−
2
√
6
)
+
125
+
48
√
6
+
30
√
6
(
5
+
2
√
6
)
=
970
© examsnet.com
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