The sum of real values of y satisfying the 21. If equations x ^ 2 + x ^ 2 * y ^ 2 + x ^ 2 * y ^ 4 = 525 and x + xy + x * y ^ 2 = 35 is

We are given the following system of equations:

1. \( x^2 + x^2 y^2 + x^2 y^4 = 525 \)
2. \( x + xy + x y^2 = 35 \)

We need to find the sum of the real values of \( y \) that satisfy these equations.

### Step 1: Simplify the first equation
The first equation can be factored as:

\[
x^2(1 + y^2 + y^4) = 525
\]

Dividing both sides by \( x^2 \) (assuming \(

Explore how to solve a system of quadratic equations involving polynomials. This problem involves factoring and quadratic equation formulas, aimed at advanced high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation