SOLUTION: if a^2 + 1 = a find the value of a^3.

Click here to see ALL problems on Equations

Question 1087364: if a^2 + 1 = a find the value of a^3.

Found 4 solutions by jim_thompson5910, Edwin McCravy, MathTherapy, ikleyn:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
Start with the given equation

Subtract 1 from both sides

Simplify. Call this equation (1)

Go back to the original equation

Multiply both sides by 'a'

Distribute

Subtract 'a' from both sides to isolate the a^3 term

Simplfy

Replace the with . See equation (1) above.

Simplify. Note how the 'a' terms on the right side cancel out

----------------------------------------------------------------------

An alternative is to solve for 'a' using the quadratic formula (after you get everything to one side and have ). That leads to two complex solutions in the form . After cubing both sides of the two equations you'll lead to . This method is a lot longer than the first method so I find it ideal to follow the first method.

----------------------------------------------------------------------

No matter which method you follow, the final answer is -1

Answer by Edwin McCravy(20054)   (Show Source):
You can put this solution on YOUR website!

if a^2 + 1 = a find the value of a^3. a� + 1 = a a� - a + 1 = 0 We recognize the left side as one of the factors in the factorization of the sum of two cubes a� + 1 = (a + 1)(a� - a + 1) So we multiply both sides by (a + 1) (a + 1)(a� - a + 1) = 0(a + 1) a� + 1 = 0 a� = -1 Edwin

Answer by MathTherapy(10552)   (Show Source):
You can put this solution on YOUR website!

if a^2 + 1 = a find the value of a^3.

------- Multiplying each side by a

Answer by ikleyn(52780)   (Show Source):
You can put this solution on YOUR website!
.

What is interesting in this problem (and why I am writing these lines) is that = -1 , BUT a =/= -1 (!!). The value of "a" in this problem is one of the two complex cubic roots of -1.