Find all real numbers a that satisfy

1/(a^3 + 7) - 7 = -a^3/(a^3 + 7) + 5.

Guest Jul 28, 2022

#1**0 **

Solve for a:

1/(a^3 + 7) - 7 = 5 - a^3/(a^3 + 7)

Bring 1/(a^3 + 7) - 7 together using the common denominator a^3 + 7. Bring 5 - a^3/(a^3 + 7) together using the common denominator a^3 + 7:

(-7 a^3 - 48)/(a^3 + 7) = (4 a^3 + 35)/(a^3 + 7)

Multiply both sides by a^3 + 7:

-7 a^3 - 48 = 4 a^3 + 35

Subtract 4 a^3 - 48 from both sides:

-11 a^3 = 83

Divide both sides by -11:

a^3 = -83/11

Taking cube roots gives (-83/11)^(1/3) times the third roots of unity:

**a = (-83/11)^(1/3) or a = -(83/11)^(1/3) or a = -(-1)^(2/3) (83/11)^(1/3)**

Guest Jul 29, 2022