What are the solutions to the equation a^5+a^2=36 ?

The solutions to the equation a^5+a^2=36 are a=2

Find the zeros of a^5+a^2=36

The zeros of a^5+a^2=36 are a=2

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a^{5} + a^{2} = 36

a = 2

Solution steps

a^{5} + a^{2} = 36

Move

36

to the left side

a^{5} + a^{2} - 36 = 0

Factor

a^{5} + a^{2} - 36 : (a - 2) (a^{4} + 2 a^{3} + 4 a^{2} + 9 a + 18)

(a - 2) (a^{4} + 2 a^{3} + 4 a^{2} + 9 a + 18) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

a - 2 = 0 or a^{4} + 2 a^{3} + 4 a^{2} + 9 a + 18 = 0

Solve

a - 2 = 0 : a = 2

Solve

a^{4} + 2 a^{3} + 4 a^{2} + 9 a + 18 = 0 :

No Solution for

a \in R

The solution is

a = 2

x^{3} - 100 = 0

9 = x^{3} + 1

60 x^{4} + 120 x^{3} - 900 x^{2} = 0

x^{3} - 7 x^{2} + 24 x - 18 = 0

x^{7} + x^{6} = 0

What are the solutions to the equation a^5+a^2=36 ?
The solutions to the equation a^5+a^2=36 are a=2
Find the zeros of a^5+a^2=36
The zeros of a^5+a^2=36 are a=2