What are the solutions to the equation (x)=(x^3+x)(x^3+x^4) ?

The solutions to the equation (x)=(x^3+x)(x^3+x^4) are x=0,x\approx 0.72449…,x\approx-1.22074…

Find the zeros of (x)=(x^3+x)(x^3+x^4)

The zeros of (x)=(x^3+x)(x^3+x^4) are x=0,x\approx 0.72449…,x\approx-1.22074…

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(x) = (x^{3} + x) (x^{3} + x^{4})

x = 0, x \approx 0.72449 \dots, x \approx - 1.22074 \dots

Solution steps

(x) = (x^{3} + x) (x^{3} + x^{4})

Switch sides

(x^{3} + x) (x^{3} + x^{4}) = (x)

Move

(x)

to the left side

(x^{3} + x) (x^{3} + x^{4}) - x = 0

Factor

(x^{3} + x) (x^{3} + x^{4}) - x : x (x^{6} + x^{5} + x^{4} + x^{3} - 1)

x (x^{6} + x^{5} + x^{4} + x^{3} - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x^{6} + x^{5} + x^{4} + x^{3} - 1 = 0

Solve

x^{6} + x^{5} + x^{4} + x^{3} - 1 = 0 : x \approx 0.72449 \dots, x \approx - 1.22074 \dots

The solutions are

x = 0, x \approx 0.72449 \dots, x \approx - 1.22074 \dots

y, x = (y + 1)^{3} - 2

3 x (4 x - 5) (x^{2} + 25) = 0

0 = x^{3} - 11 x^{2} + 37 x - 42

x, y^{2} - 12 x^{3} = 8 y

x^{4} - 7 x^{3} + 13 x^{2} + 3 x - 18 = 0

What are the solutions to the equation (x)=(x^3+x)(x^3+x^4) ?
The solutions to the equation (x)=(x^3+x)(x^3+x^4) are x=0,x\approx 0.72449…,x\approx-1.22074…
Find the zeros of (x)=(x^3+x)(x^3+x^4)
The zeros of (x)=(x^3+x)(x^3+x^4) are x=0,x\approx 0.72449…,x\approx-1.22074…