Question

For what value of m, m×m×m+3×m×m+2m+9 is a perfect cube?

Answer 1

Answer:

To find: for what value of mm , the given term is a perfect cube

Solution:

\therefore m^{3}+3m^{2}+2m+9∴m

3

+3m

2

+2m+9

=m^{3}+3m^{2}+3m+1-m+8=m

3

+3m

2

+3m+1−m+8

=(m+1)^{3}-m+8=(m+1)

3

−m+8

We see that (m+1)^{3}(m+1)

3

is a perfect cube, but not the given term because of (-m+8)(−m+8) . So we equate it with 00 (zero).

Thus, -m+8=0−m+8=0

\Rightarrow m=8⇒m=8

When m=8m=8 , the value of the given term is 729729 , perfect cube of 99 .

Answer: the value of mm is 88 for which m^{3}+3m^{2}+2m+9m

3

+3m

2

+2m+9 is a perfect cube.