Question

Which values of a and b make the following equation true?

(5x² 7²) (-4x²,5) =-20x²go
A) a = 11, b = 7
B) a = 11, b = 10
C) a= 28, b= 7
D) a = 28, b =10

Answer 1

To make the equation true, we need to solve the polynomial equation -100x^6 + 125x^4 + 4.5x^2 - 25 = 0. This equation can be solved using advanced algebraic techniques.

Step-by-step explanation:

In this case, we have the equation (5x² + 7²)(-4x² + 5) = -20x². To find the values of a and b that make the equation true, we can expand the expression on the left side of the equation:

Using the rule (xa)b = xa.b, we can rewrite the equation as (25x^4 - 30x^2 + 49)(-4x^2 + 5) = -20x². Expanding further, we get -100x^6 + 125x^4 - 98x^2 + 122.5x^2 - 25 = -20x^2.

Combining like terms, we have -100x^6 + 125x^4 + 24.5x^2 - 25 = -20x^2. Simplifying further, we get -100x^6 + 125x^4 + 4.5x^2 - 25 = 0.

This equation is a polynomial equation of degree 6. To solve it, we need to use advanced algebraic techniques such as factoring, synthetic division, or numerical methods.