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Answer 1

$\bf{\large{\underline{\underline{Question:-}}}}$

If a + b = 12 and ab = 27, find the value of a³ + b³.

$\bf{\large{\underline{\underline{Answer:-}}}}$

$\large{\boxed{ \tt {a}^{3} + {b}^{3}= 756}}$

$\bf{\large{\underline{\underline{Explanation:-}}}}$

Given :- a + b = 12

ab = 27

To find : a³ + b³

Solution :-

$\tt a + b = 12$

Cubing on both sides

$\tt {(a + b)}^{3} = {(12)}^{3}$

We know that (x + y)³ = x³ + y³ + 3xy(x + y)

Here x = a, y = b

By substituting the values in the identity we have

$\tt {a}^{3} + {b}^{3} + 3ab(a + b) = 1728$

$\tt {a}^{3} + {b}^{3} + 3(27)(a + b) = 1728$

[Since given that ab = 27]

$\tt {a}^{3} + {b}^{3} + 81(a + b) = 1728$

$\tt {a}^{3} + {b}^{3} + 81(12) = 1728$

[Since given that a + b = 12]

$\tt {a}^{3} + {b}^{3} + 972 = 1728$

$\tt {a}^{3} + {b}^{3}= 1728 - 972$

$\tt {a}^{3} + {b}^{3}= 756$

$\Huge{\boxed{ \tt {a}^{3} + {b}^{3}= 756}}$

Answer 2

Question : If a + b = 12 and ab = 27, find the value of a³ + b³.

Step-by-step explanation:

Given :

a + b = 12

a + b = 12 ab = 27

let's have a look on the below Identity :

• a³ + b ³ = (a + b ) ( a² + b² - ab )

• a³ + b ³ = (a + b ) ( a² + b² - ab ) ( a + b ) ²- 2ab = a² + b²

Therefore ,

a³ + b³= ( a + b ){ ( a + b )² - 3ab }

Now , let's insert the values :

Hence ,

a³ + b³ = 12{12²- 3 ×27 }

=> 12 { 144- 3×27 }

=> 12×63

=> 756 ( Answer )

a³ + b³ = 756