Question

What is the solution to the equation 5/3b^3-2b^2-5 = 2/b^3-2?

a. b = –4 and b = 0
b. b = –4
c. b = 0 and b = 4
d. b = 4

Answer 1

To solve the equation, we can use the quadratic formula and find the solutions for b.

Step-by-step explanation:

To solve the equation 5/3b^3 - 2b^2 - 5 = 2/b^3 - 2, we need to find the values of b that satisfy the equation. To do this, we can cross-multiply and rearrange the equation to get a quadratic equation in terms of b. Using the quadratic formula, which states that b = (-b ± √(b^2 - 4ac)) / 2a, we can find the solutions for b.

Substituting the values a = 5/3, b = -2, and c = -7 into the quadratic formula, we obtain the solutions b = -4 and b = 0.

Therefore, the solution to the equation 5/3b^3 - 2b^2 - 5 = 2/b^3 - 2 is b = -4 and b = 0.

Answer 2

The solution to the equation is:

Option c. b=0 and b=4

Step-by-step explanation:

5 / (3b^3-2b^2-5) = 2 / (b^3-2)

Cross multiplication:

5(b^3-2)=2(3b^3-2b^2-5)

Applying distributive property both sides of the equation to eliminate the parentheses:

5(b^3)-5(2)=2(3b^3)-2(2b^2)-2(5)

Multiplying:

5b^3-10=6b^3-4b^2-10

Passing all the terms to the right side of the equation: Subtracting 5b^3 and adding 6 both sides of the equation:

5b^3-10-5b^3+10=6b^3-4b^2-10-5b^3+10

Adding like terms:

0=b^3-4b^2

b^3-4b^2=0

Getting common factor b^2 on the left side of the equation:

b^2 (b^3/b^2-4b^2/b^2)=0

b^2 (b-4) = 0

Two solutions:

(1) b^2=0

Solving for b: Square root both sides of the equation:

sqrt(b^2)=sqrt(0)

Square root:

b=0

(2) b-4=0

Solving for b: Adding 4 both sides of the equation:

b-4+4=0+4

Adding like terms:

b=4

The solution of the equation is: b=0 and b=4 (Option c)