The value of \(\frac{(2.3)^3 + 0.027}{(2.3)^3 - 0.69 + 0.09}\) is
2.6
Let the given expression be denoted as E. We have:
E = \(\frac{(2.3)^3 + 0.027}{(2.3)^3 - 0.69 + 0.09}\)
We notice that \(0.027 = (0.3)^3\) and \(0.69 = 2.3 \times 0.3\). Substituting these values, we get:
E = \(\frac{(2.3)^3 + (0.3)^3}{(2.3)^3 - 2.3 \times 0.3 + (0.3)^2}\)
This expression resembles the sum of cubes formula: \(a^3 + b^3 = (a+b)(a^2 - ab + b^2)\), where \(a = 2.3\) and \(b = 0.3\).
Therefore, the numerator is \( (2.3 + 0.3)((2.3)^2 - 2.3 \times 0.3 + (0.3)^2) \).
Simplifying, we have:
E = \(\frac{(2.3 + 0.3)((2.3)^2 - 2.3(0.3) + (0.3)^2)}{(2.3)^2 - 2.3(0.3) + (0.3)^2} = 2.3 + 0.3 = 2.6\)
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