Question

If a - b = 2 and ab = 24, then what is the value of a3 - b3?

Answer 1

$\textbf{\huge{ANSWER:}}$

Given:

a - b = 2

ab = 24

To find:

$a^{3} - b^{3}$

Identity to be used:

$(a - b)^{3} = a^{3} - b^{3} - 3ab (a - b)$

Put the values directly in the formula:

=》 $2^{3} = a^{3} - b^{3} - 3(24)(2)$

=》 $8 = a^{3} - b^{3} - 144$

=》 $a^{3} - b^{3} = 144 + 8$

=》 $a^{3} - b^{3} = 152$

Hope it Helps!! :)

Answer 2

Answer :

The value of a³ - b³ is 152.

Step-by-step explanation :

a - b = 2

ab = 24

Using identity here :

( a - b )³ = a³ - b³ - 3ab ( a - b )

⇒ ( 2 )³ = a³ - b³ - 3 × 24 ( 2 )

⇒ 8 = a³ - b³ - 72 ( 2 )

⇒ a³ - b³ = 8 + 144

⇒ a³ - b³ = 152.

Hence, the value of a³ - b³ is 152.