High School

Which equation can be solved by using this system of equations?

A. [tex]3x^3 - 7x^2 - 5 = 0[/tex]

B. [tex]3x^3 - 7x^2 - 5 = 7x^4 - 2x[/tex]

C. [tex]7x^4 - 2x = 0[/tex]

D. [tex]7x^4 - 3x^3 - 7x^2 - 2x - 5 = 0[/tex]

Answer :

Final answer:

The equation that can be solved using this system of equations is (c) 7x^4 - 2x = 0. To solve this equation, we can set the equation equal to zero and then factor out the common term x. Therefore, the equation can be solved by setting each factor equal to zero: x = 0 and x^3 - 2 = 0.

Explanation:

The equation that can be solved using this system of equations is (c) 7x^4 - 2x = 0.

To solve this equation, we can set the equation equal to zero and then factor out the common term x:

7x(x^3 - 2) = 0

Therefore, the equation can be solved by setting each factor equal to zero:
x = 0
x^3 - 2 = 0

Simplifying the second equation, we get:
x^3 = 2

Taking the cube root of both sides, we find:
x = ∛2

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