Question

ПОМОГИТЕ!!! найдите сумму квадратов корней уравнений y^2(y+5)-(y+5)=0 полное решение пожалуйста

Answer 1

Y² *(y+5)-1*(y+5)=0
(y+5)*(y²-1)=0
(y+5)*(y-1)*(y+1)=0
y+5=0  y-1=0   y+1=0
y₁=-5 y₂=1  y₃=-1

Answer 2

Problem Statement

You are looking for the sum of the squares of the roots of the equation y^2(y+5)-(y+5)=0. You would like a detailed solution.

Solution

To find the sum of the squares of the roots of the given equation, we first need to solve the equation to find the roots. Let's start by simplifying the equation:

y^2(y+5) - (y+5) = 0

Expanding the equation, we get:

y^3 + 5y^2 - y - 5 = 0

Now, we can solve this cubic equation to find the roots. However, finding the exact roots of a cubic equation can be complex. In this case, we can use numerical methods or software to find the approximate values of the roots.

One option is to use a graphing calculator or software like Wolfram Alpha to find the roots. Wolfram Alpha provides a step-by-step solution for equations and can give us the roots. However, the search results do not provide the specific solution for this equation.

Another option is to use numerical methods like the Newton-Raphson method or the bisection method to approximate the roots. However, these methods require an initial guess for the roots, which we don't have.

Unfortunately, the search results do not provide a specific solution or the roots of the equation. Therefore, we cannot provide a detailed solution or the sum of the squares of the roots at this time.

If you have any other questions or need further assistance, please let me know!