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Alika [10]
2 years ago
9

The sum of a positive number and 56 times its reciprocal is equal to its cube. What is the number?

Mathematics
1 answer:
cricket20 [7]2 years ago
7 0

Answer:

2×sqrt(2) = 2.828427125...

Step-by-step explanation:

x = "a positive number"

x + 56/x = x³

x² + 56 = x⁴

x⁴ - x² - 56 = 0

(x² + 7)(x² - 8) = 0

this is true only for

x² = -7

or

x² = 8

x² = -7 would mean that x is an imaginary number. so, that is not a valid solution here.

x² = 8 means

x = sqrt(8) = sqrt(4×2) = 2×sqrt(2) = 2.828427125...

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Add 10z to both sides

7z + 7 = -7

Subtract 7 from both sides

7z = -14

Divide by 7

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Step-by-step explanation:

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3 years ago
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