Question

Х^2+5х/7 = 2. У відповідь запишіть добуток одержаних коренів.​

Answer 1

Якщо я не помиляюсь то якось так.....

Answer 2

Solving the Equation

To solve the equation x^2 + 5x/7 = 2, we can start by multiplying both sides of the equation by 7 to eliminate the fraction:

7(x^2 + 5x/7) = 7(2)

Simplifying the equation gives us:

7x^2 + 5x = 14

Now, let's rearrange the equation to bring all terms to one side:

7x^2 + 5x - 14 = 0

Finding the Roots

To find the roots of the equation, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, the coefficients of the quadratic equation are:

a = 7 b = 5 c = -14

Substituting these values into the quadratic formula, we get:

x = (-5 ± √(5^2 - 4 * 7 * -14)) / (2 * 7)

Simplifying further:

x = (-5 ± √(25 + 392)) / 14

x = (-5 ± √417) / 14

The two possible solutions for x are:

x = (-5 + √417) / 14 x = (-5 - √417) / 14

Product of the Roots

To find the product of the roots, we can multiply the two solutions together:

Product = ((-5 + √417) / 14) * ((-5 - √417) / 14)

Simplifying the expression:

Product = (-5^2 - √417 * 5 + √417 * -5 - √417 * √417) / 14^2

Product = (25 - 5√417 - 5√417 - 417) / 196

Product = (25 - 10√417 - 417) / 196

Product = (-392 - 10√417) / 196

Therefore, the product of the roots of the equation x^2 + 5x/7 = 2 is (-392 - 10√417) / 196.

Please note that the provided search snippet does not contain relevant information for solving this specific equation. However, the solution process outlined above is a standard method for solving quadratic equations.