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Byju's Answer
Standard XII
Mathematics
One - One function
If a and ...
Question
If
a
and
b
are positive integers such that
(
a
2
−
b
2
)
is a prime number, then
A
a
2
−
b
2
=
(
a
+
b
)
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B
a
2
−
b
2
=
a
−
b
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C
a
2
+
b
2
=
a
−
b
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D
a
2
+
b
2
=
a
+
b
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Solution
The correct option is
A
a
2
−
b
2
=
(
a
+
b
)
if
a
and
b
are positive numbers,
then
(
a
+
b
)
will also be a positive number.
a
2
−
b
2
=
(
a
+
b
)
(
a
−
b
)
it is given that (
a
2
−
b
2
) is a prime number so, its factors can be only
1
and itself,
and
(
a
+
b
)
is a positive integer so,
(
a
−
b
)
should be equal to
1
a
2
−
b
2
=
(
a
+
b
)
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0
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