Cube root (3p + 7) - cube root (2p - 1) = 0 #solve the equations.

Question

Cube root (3p + 7) - cube root (2p - 1) = 0  #solve the equations.

Answer 1

Move the negative term to the right side of the equation.

 

³√(3p + 7) = ³√(2p - 1)

 

 

Now, cube both sides of the equation to undo the cube-root.  Or just set the arguments equal to each other.

 

3p + 7 = 2p - 1

 

Solve for p.

 

 

Another way you can approach this is to realize when you add two inverses, the sum is always zero.  So if you set the arguments equal to each other, the inverse terms will be equal in value.  Just with opposite signs.

 

If       ³√(a) - ³√(a) = 0

 

Then,     3p + 7 = a = 2p - 1

 

 

Answer 2

Cube root (3p + 7) - cube root (2p - 1) = 0

cube each side to get:

3p+7-2p+1=0^3        (0^3=0)

p+8=0

p=-8

it helps after solving an equation like this to plug in the value to double check the answer

which gives you 0 in this case