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Question

Accepted Answer

Let x = 0.58. The expression becomes (x³ − 0.001) / (x² + 0.058 + 0.01).

First, note that 0.001 = (0.1)³.
So, numerator: x³ − (0.1)³
Denominator: x² + 0.058 + 0.01 = x² + 0.058 + 0.01 = x² + 0.058x + 0.01 (but 0.058 is not 0.058x, so let's check carefully)

But 0.58 × 0.58 = 0.3364
So denominator: 0.3364 + 0.058 + 0.01 = 0.3364 + 0.058 = 0.3944; 0.3944 + 0.01 = 0.4044

Numerator: 0.58 × 0.58 × 0.58 = 0.195112; 0.195112 − 0.001 = 0.194112

So, the expression is 0.194112 / 0.4044

Now, divide:
0.194112 ÷ 0.4044 ≈ 0.48

Therefore, the answer is 0.48.

Alternatively, you can recognize the numerator as a³ − b³ and the denominator as a² + ab + b², where a = 0.58, b = 0.1. So, (a³ − b³)/(a² + ab + b²) = a − b = 0.58 − 0.1 = 0.48.

Thus, the answer is 0.48.

Answer

Answer

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