If we multiply a fraction by itself and divide to product by its reciprocal, the fraction thus obtained is 18 26/27. What is the original fraction?
- 3.66
- 2.67
- 1.33
- None of these
Explanation
We know that:
x × x = x²
Reciprocal of x = 1/x
According to the problem:
(x × x) ÷ (1/x) = 18/26 × 27
Simplifying the equation:
x² ÷ (1/x) = 18/26 × 27
x³ = 18/26 × 27
Now, let's solve for x:
x³ = 486/26
x³ = 18.69 (approximately)
x = ∛(18.69) ≈ 2.67
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