Question

Известно (х+1/х)²=3 Чему равно значение суммы х³+1/х³ ?

Answer 1

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Answer 2

Solution:

The given equation is (x + 1/x)² = 3. We need to find the value of the sum x³ + 1/x³.

To solve this, we can use the following formula: x³ + 1/x³ = (x + 1/x)³ - 3(x + 1/x)

Let's calculate the value using this formula.

Calculation:

Using the given equation (x + 1/x)² = 3, we can find (x + 1/x) by taking the square root of both sides: (x + 1/x) = ±√3

Now, we can substitute this value into the formula: x³ + 1/x³ = (x + 1/x)³ - 3(x + 1/x)

Substitute (x + 1/x) = ±√3 into the formula: x³ + 1/x³ = (±√3)³ - 3(±√3)

Simplify the expression: x³ + 1/x³ = (±√27) - 3(±√3)

Finally, we get: x³ + 1/x³ = ±3√3 - 3√3

So, the value of the sum x³ + 1/x³ is ±3√3 - 3√3.

Conclusion:

Therefore, the value of the sum x³ + 1/x³ is ±3√3 - 3√3.