Question

If a + b is equal to 11 and a square + b square is equal to 61 find the value of a cube plus b cube

Answer 1

$\bf HELLO DEAR, \\ \\ \bf given that:- (a + b) = 11 , (a^{2} + b^{2}) = 61 \\ \\ \bf now, \\ \\ \bf (a + b)^{2} = (11)^{2} \\ \\ \bf a^{2} + b^{2} + 2ab = 121 \\ \\ \bf 2ab = 121 - 61 \\ \\ \bf 2ab = 60 \\ \\ \bf ab = 30 \\ \\ \bf \: NOW, \\ \\ \bf (a^{3} + b^{3}) = (a + b)(a^{2} + b^{2} - ab) \\ \\ \bf (a^{3} + b^{3}) = (11)(61 - 30) \\ \\ \bf (a^{3} + b^{3}) = (11)(31) \\ \\ \bf (a^{3} + b^{3}) = 341$



$\underline{\bf I \: \: HOPE \: \: ITS \: \: HELP \: \: YOU \: \: DEAR, \: \: THANKS}$

Answer 2

a + b = 11

Square on both sides,

(a + b)² = 11²

a² + b² + 2ab = 121

61 + 2ab = 121

2ab = 121 - 61

$2ab = 60 \\ \\ ab = \frac{60}{2} \\ \\ ab = 30$


Then,


$( {a}^{3} + {b}^{3} ) = (a + b)( {a}^{2} - ab + {b}^{2} ) \\ \\ {a}^{3} + {b}^{3} = (11)(61 - 30) \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = (11)(31) = 341$



I hope this will help you
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