What are the solutions to the equation a^3+a^2=a^5 ?

The solutions to the equation a^3+a^2=a^5 are a=0,a\approx 1.32471…

Find the zeros of a^3+a^2=a^5

The zeros of a^3+a^2=a^5 are a=0,a\approx 1.32471…

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a^{3} + a^{2} = a^{5}

a = 0, a \approx 1.32471 \dots

Solution steps

a^{3} + a^{2} = a^{5}

Switch sides

a^{5} = a^{3} + a^{2}

Move

a^{2}

to the left side

a^{5} - a^{2} = a^{3}

Move

a^{3}

to the left side

a^{5} - a^{2} - a^{3} = 0

Factor

a^{5} - a^{2} - a^{3} : a^{2} (a^{3} - a - 1)

a^{2} (a^{3} - a - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

a = 0 or a^{3} - a - 1 = 0

Solve

a^{3} - a - 1 = 0 : a \approx 1.32471 \dots

The solutions are

a = 0, a \approx 1.32471 \dots

x^{4} + 36 = 13 x^{2}

x^{3} + x + 3 = x^{2}

x^{2} = 14 x^{6}

q^{4} - q^{2} - 6 = 0

(x^{2} + 6 x - 7) (2 x^{2} - 5 x - 3) = 0

What are the solutions to the equation a^3+a^2=a^5 ?
The solutions to the equation a^3+a^2=a^5 are a=0,a\approx 1.32471…
Find the zeros of a^3+a^2=a^5
The zeros of a^3+a^2=a^5 are a=0,a\approx 1.32471…