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Byju's Answer
Standard IX
Mathematics
Zeroes of a Polynomial
If m = √15 ...
Question
If
m
=
3
√
15
and
n
=
3
√
14
, find the value
m
−
n
−
1
m
2
+
m
n
+
n
2
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Solution
Given:
m
3
=
15
,
n
3
=
14
Now, solving
m
−
n
−
1
m
2
+
m
n
+
n
2
Taking LCM,
=
m
3
+
m
2
n
+
m
n
2
−
n
m
2
−
m
n
2
−
n
3
−
1
m
2
+
m
n
+
n
2
=
m
3
−
n
3
−
1
m
2
+
m
n
+
n
2
Substituting the given values,
=
15
−
14
−
1
m
2
+
m
n
+
n
2
=
0
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2
Similar questions
Q.
If
tan
A
+
sin
A
=
m
and
tan
A
+
sin
A
=
n
then
m
2
−
n
2
=
3
√
m
n
Q.
If
m
2
+
m
′
2
+
2
m
m
′
cos
x
=
1
,
n
2
+
n
′
2
+
2
n
n
′
cos
x
=
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and
m
n
+
m
′
n
′
+
(
m
n
′
+
m
′
n
)
cos
x
=
0
, prove that
(i)
m
2
+
n
2
=
c
o
sec
2
x
(ii)
m
′
2
+
n
′
2
=
c
o
sec
2
x
Q.
Let
M
and
N
be two
3
×
3
matrices such that
M
N
=
N
M
. Further, if
M
≠
N
2
and
M
2
=
N
4
, then
Q.
(
m
+
n
)
(
m
2
−
m
n
+
n
2
)
Q.
If
m
2
+
m
′
2
+
2
m
m
′
cos
θ
=
1
,
n
2
+
n
′
2
+
2
n
n
′
cos
θ
=
1
,
and
m
n
+
m
′
n
′
+
(
m
n
′
+
m
′
n
)
=
cos
θ
=
θ
, then
prove that
m
2
+
n
2
=
csc
2
θ
.
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