Question

a cube - b cube = 27 and (a+b) whole square - ab = 9 then find (a-b) = ?

Answer 1

Step-by-step explanation:

Given :-

a³-b³ = 27

(a+b)² - ab = 9

To find :-

The value of a-b

Solution :-

Given that

(a+b)²-ab = 9

=> (a²+2ab+b²)-ab = 9

=> a²+b²+(2ab-ab) = 9

=> a²+b²+ab = 9------(1)

a³-b³ = 27

We know that

a³-b³ = (a-b)(a²+ab+b²)

Therefore

(a-b)(a²+ab+b²) = 27

=> (a-b)(9) = 27 (From (1))

=> a-b = 27/9

=> a-b = 3

Answer :-

The value of a-b is 3

Used formulae:-

→ (a+b)² = a²+2ab+b²

→ a³-b³ = (a-b)(a²+ab+b²)

Answer 2

Step-by-step explanation:

Step-by-step explanation:

Given :-

a³-b³ = 27

(a+b)² - ab = 9

To find :-

The value of a-b

Solution :-

Given that

(a+b)²-ab = 9

=> (a²+2ab+b²)-ab = 9

=> a²+b²+(2ab-ab) = 9

=> a²+b²+ab = 9------(1)

a³-b³ = 27

We know that

a³-b³ = (a-b)(a²+ab+b²)

Therefore

(a-b)(a²+ab+b²) = 27

=> (a-b)(9) = 27 (From (1))

=> a-b = 27/9

=> a-b = 3

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