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Algebra Level 2

2. 3 3 − 0.027 2. 3 2 + 0.69 + 0.09 \frac {2.3^3 - 0.027}{2.3^2 + 0.69 + 0.09}

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2 2.273 2.327 3

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1 solution

It should have been:

2. 3 3 − 0.027 2. 3 2 + 0.69 + 0.09 \dfrac{2.3^3-0.027}{2.3^2+0.69+0.09}

= ( 2. 3 3 − 0. 3 3 ) 2. 3 2 + 0.69 + 0.09 = \dfrac {(2.3^3 - 0.3^3)}{2.3^2+0.69+0.09}

= ( 2.3 − 0.3 ) ( 2. 3 2 + 0.69 + 0.09 ) 2. 3 2 + 0.69 + 0.09 = \dfrac {(2.3-0.3)(2.3^2 + 0.69+0.09)}{2.3^2+0.69+0.09}

= 2.3 − 0.3 = 2 =2.3-0.3 = \boxed{2}

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Moderator note:

Yes correct! Note that one can generalize this: a 3 − b 3 = ( a − b ) ( a 2 + a b + b 2 ) a^3 - b^3 = (a-b)(a^2 + ab + b^2) , so a − b = a 3 − b 3 a 2 + a b + b 2 a-b = \frac {a^3-b^3}{a^2 + ab + b^2} . In this case, we have a = 2.3 , b = 0.3 a = 2.3, b = 0.3 .

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