Question

X^3-7x^2=8-14x нужно решить через теорему Виета ​

Answer 1

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Объяснение:

Answer 2

Solving the Equation Using Vieta's Theorem

To solve the equation x^3 - 7x^2 = 8 - 14x using Vieta's theorem, we can first rewrite the equation in the form x^3 - 7x^2 + 14x - 8 = 0. Vieta's theorem provides a relationship between the coefficients of a polynomial and its roots. For a cubic equation of the form ax^3 + bx^2 + cx + d = 0, the sum of the roots is given by -b/a, the sum of the products of every possible pair of roots is given by c/a, and the product of the roots is given by -d/a.

Applying Vieta's Theorem to the Given Equation

1. Sum of the Roots (x1 + x2 + x3): - According to Vieta's theorem, the sum of the roots of the cubic equation ax^3 + bx^2 + cx + d = 0 is given by -b/a.

2. Sum of the Products of Every Possible Pair of Roots (x1x2 + x1x3 + x2x3): - According to Vieta's theorem, the sum of the products of every possible pair of roots of the cubic equation ax^3 + bx^2 + cx + d = 0 is given by c/a.

3. Product of the Roots (x1 * x2 * x3): - According to Vieta's theorem, the product of the roots of the cubic equation ax^3 + bx^2 + cx + d = 0 is given by -d/a.

Conclusion

By applying Vieta's theorem to the given equation, we can find the sum of the roots, the sum of the products of every possible pair of roots, and the product of the roots. These values can provide insights into the nature of the roots and aid in solving the equation.