Question

If a-b =3 and ab =4 ,find a^3-b^3

Answer 1

Answer:

63

Step-by-step explanation:

 ( x - y )^3 = x^3 - y^3 - 3xy( x - y )

Here,

⇒ a - b = 3

  Cube on both sides:

⇒ ( a - b )^3 = 3^3

⇒ a^3 - b^3 - 3ab( a - b ) = 27

     ab = 4 , a - b = 3

⇒ a^3 - b^3 - 3( 4 )( 3 ) = 27

⇒ a^3 - b^3 - 36 = 27

⇒ a^3 - b^3 = 27 + 36

⇒ a^3 - b^3 = 63

Answer 2

ANSWER:

• Value of the above expression = 63

GIVEN:

• a-b = 3 ......(i)
• ab = 4 .....(ii)

TO FIND:

• Value of (a³-b³)

SOLUTION:

=> a-b = 3

Squaring both sides we get;

=> (a-b)² = (3)²

=> a²+b²-2ab = 9

Putting ab = 4 from (ii).

=> a²+b²-2(4) = 9

=> a²+b² = 9+8

=> a²+b² = 17

Formula:

• a³-b³ = (a-b)(a²+b²+ab)

Putting the values in the formula.

=> a³-b³ = 3(17+4)

=> a³-b³ = 3(21)

=> a³-b³ = 63

NOTE:

Some important formulas:

(a+b)² = a²+b²+2ab

(a-b)² = a²+b²-2ab

(a+b)(a-b) = a²-b²

(a+b)³ = a³+b³+3ab(a+b)

(a-b)³ = a³-b³-3ab(a-b)

a³+b³ = (a+b)(a²+b²-ab)

a³-b³ = (a-b)(a²+b²+ab)

(a+b)² = (a-b)²+4ab

(a-b)² = (a+b)²-4ab