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Standard VIII
Mathematics
Question
If
x
=
(
2
+
√
5
)
1
/
2
+
(
√
5
−
2
)
1
/
2
and
y
=
(
2
+
√
5
)
1
/
2
−
(
√
5
−
2
)
1
/
2
,
then evaluate
x
2
+
y
2
.
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Solution
Verified by Toppr
a
b
↑
↑
x
=
(
2
+
√
5
)
1
/
2
+
(
√
5
−
2
)
1
/
2
y
=
(
(
2
+
√
5
)
)
1
/
2
−
(
√
5
−
2
)
1
/
2
i.e
x
=
a
1
/
2
+
b
1
/
2
y
=
a
1
/
2
−
b
1
/
2
So
x
2
+
y
2
=
a
+
b
+
2
a
1
/
2
b
1
/
2
+
a
+
b
−
2
a
1
/
2
b
1
/
2
=
2
(
a
+
b
)
=
2
(
2
+
√
5
+
√
5
−
2
)
=
2.2
√
5
=
4
√
5
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5
Similar Questions
Q1
If
x
=
(
2
+
√
5
)
1
/
2
+
(
√
5
−
2
)
1
/
2
and
y
=
(
2
+
√
5
)
1
/
2
−
(
√
5
−
2
)
1
/
2
,
then evaluate
x
2
+
y
2
.
View Solution
Q2
Evaluate:
[
(
4
)
1
4
×
(
2
)
1
2
×
(
5
)
1
5
]
0
View Solution
Q3
If
y
=
7
5
(
1
+
1
10
2
+
1
⋅
3
1
⋅
2
1
10
4
+
1
⋅
3
⋅
5
1
⋅
2
⋅
3
1
10
6
+
⋯
∞
)
then
4
y
2
=
View Solution
Q4
If
x
∗
y
=
√
x
2
+
y
2
, then the value of
(
1
∗
2
√
2
)
(
1
∗
−
2
√
2
)
is:
View Solution
Q5
Solve:
5
1
3
−
[
2
1
3
÷
{
3
4
−
1
2
×
(
7
10
−
3
5
)
}
]
View Solution