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Byju's Answer
Standard VIII
Mathematics
Finding Square Root through Repeated Subtraction
Let a and b b...
Question
Let a and b be positive integers such that ab+1 divides a2+b2. Why must a2+b2ab+1 be a perfect square?
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5
Similar questions
Q.
Let
a
,
b
,
c
be positive integers such that a divides
b
2
, b divides
c
2
and c divides
a
2
. Prove that
a
b
c
divides
(
a
+
b
+
c
)
7
Q.
Let
a
,
b
are positive integers such that
a
2
−
b
2
=
7
then find
a
,
b
.
Q.
Let a, b, c be positive real numbers. The sequence
(
a
n
)
n
≥
1
is defined by
a
1
=
a
,
a
2
=
b
and
a
n
+
1
=
a
2
n
+
c
a
n
−
1
for all
n
≥
2.
Prove that the terms of the sequence are all positive integers if and only if a,b and
a
2
+
b
2
+
c
a
b
are positive integers.
Q.
If A and B be square matrices of the same order such that AB=BA, then show that (A+B)
2
=A
2
+2AB+B
2
.
Q.
Let
a
and
b
be two positive real numbers such that
a
+
2
b
≤
1
. Let
A
1
and
A
2
be respectively, the areas of circles with radii
a
b
3
and
b
2
. Then the maximum possible value of
A
1
A
2
is
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