Question

using suitable identity, evaluate 13^3 - 6^3 - 7^3​

Answer 1

$Question \: = > \: \:$

${13}^{3} - {6}^{3} - {7}^{3}$

$Answer \: = > \:$

${a}^{3} + {b}^{3} + {c}^{3} = 3abc$

[If a+b+c=0]

a = 13 , b=-6 , c=-7

13-6-7 => 13-13 => 0

$Therefore \: \: {a}^{3} + {b}^{3} + {c}^{3} = 3abc$

= 3.13.(-6).(-7)

= 39(42)

= 1638

$\boxed{Answer \: = > \: 1638}$

Answer 2

Answer:

1638

Step-by-step explanation:

Question=>

{13}^{3} - {6}^{3} - {7}^{3}13

3

−6

3

−7

3

Answer \: = > \:Answer=>

{a}^{3} + {b}^{3} + {c}^{3} = 3abca

3

+b

3

+c

3

=3abc

[If a+b+c=0]

a = 13 , b=-6 , c=-7

13-6-7 => 13-13 => 0

Therefore \: \: {a}^{3} + {b}^{3} + {c}^{3} = 3abcThereforea

3

+b

3

+c

3

=3abc

= 3.13.(-6).(-7)

= 39(42)

= 1638