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

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

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

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

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

x = 0, x \approx 1.32471 \dots

Solution steps

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

Switch sides

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

Move

x^{3}

to the left side

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

Move

x^{2}

to the left side

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

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

The solutions are

x = 0, x \approx 1.32471 \dots

3 x^{4} + 4 x^{3} - 12 x^{2} + 10 = 0

(x) = x^{3} - 3 x^{2} - 9 x - 5

x, x^{2} + (y - c b r t (x^{2}))^{2} = 25

x^{3} - 2 x^{2} + 2 x + 5 = 0

9 x^{4} - 19 x^{2} + 2 = 0

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