Question

Calculate the value of 83^3+17^3 divided by 83^2-83×17+17^3

Answer 1

$we \: know \: that \: {a}^{3} + {b}^{3} = (a + b)( {a}^{2} - ab + {b}^{2} ) \\ therefore \: \frac{ {83}^{3} + {17}^{3} }{ {83}^{2} - 83 \times 17 + {17}^{2} } = \frac{(83 + 17)( {83}^{2} - 83 \times 17 + {17}^{2} ) }{{83}^{2} - 83 \times 17 + {17}^{2} } \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 83 + 17 = 100$

Answer 2

we know that a

3

+b

3

=(a+b)(a

2

−ab+b

2

)

therefore

83

2

−83×17+17

2

83

3

+17

3

=

83

2

−83×17+17

2

(83+17)(83

2

−83×17+17

2

)

=83+17=100