Solve
Guides
Join / Login
Use app
Login
0
You visited us
0
times! Enjoying our articles?
Unlock Full Access!
Standard XII
Mathematics
Question
Positive integers a and b are such that a+b=a/b +b/a . What is the value of
a
2
+
b
2
?
Open in App
Solution
Verified by Toppr
a
+
b
=
a
/
b
+
b
/
a
⟹
a
+
b
=
a
2
+
b
2
a
b
a
2
b
+
a
b
2
=
a
2
+
b
2
a
2
(
b
−
1
)
+
b
2
(
a
−
1
)
=
0
∵
a
,
b
are positive integers
,
a
2
,
b
2
can't be zero
⟹
a
−
1
=
0
⟹
a
=
1
,
b
−
1
=
0
⟹
b
=
1
a
2
+
b
2
=
1
+
1
=
2
Was this answer helpful?
6
Similar Questions
Q1
Positive integers a and b are such that a+b=a/b +b/a . What is the value of
a
2
+
b
2
?
View Solution
Q2
Let
a
,
b
are positive integers such that
a
2
−
b
2
=
7
then find
a
,
b
.
View Solution
Q3
If
a
and
b
are positive integers such that
(
a
2
−
b
2
)
is a prime number, then
View Solution
Q4
If
a
and
b
are positive integers,
f
is a function defined for positive numbers and attains only positive values such that
f
(
y
f
(
x
)
)
=
x
a
y
b
, then
View Solution
Q5
Suppose
b
is a positive integer such that
2
4
b
2
is also an integer. What are the possible values of
b
?
View Solution