Question

prove that (0.9*0.9*0.9+0.4*0.4*0.4)/(0.9*0.9-0.9*0.4+0.4*0.4)=1​

Answer 1

Step-by-step explanation:

$\frac{0.96 \times 0.96 \times 0.96 + 0.4 \times 0.4 \times 0.4}{0.96 \times 0.96 - 0.96 \times 0.4 + 0.4 \times 0.4} \\ \\ = \frac{ {0.96}^{3} + {0.4}^{3} }{ {0.96}^{2} - 0.96 \times 0.4 + {0.4}^{2} } \\ since \: we \: know \: that \\ {x}^{3} + {y}^{3} = (x + y)( {x}^{2} - xy + {y}^{2} ) \\ = \frac{(0.96 + 0.4)( {0.96}^{2} - 0.96 \times 0.4 + {0.4}^{2})}{ ({0.96}^{2} - 0.96 \times 0.4 + {0.4}^{2}) } \\ \\ = 0.96 + 0.4 \\ = 1.00 = 1 \: \: \: \: \: \: \: (hence \: proved)$

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