What are the solutions to the equation (x^2-x-3)^2-2(x^2-x)+3=0 ?

The solutions to the equation (x^2-x-3)^2-2(x^2-x)+3=0 are x=-1,x=3,x=-2,x=2

Find the zeros of (x^2-x-3)^2-2(x^2-x)+3=0

The zeros of (x^2-x-3)^2-2(x^2-x)+3=0 are x=-1,x=3,x=-2,x=2

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

x = - 1, x = 3, x = - 2, x = 2

Solution steps

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

Expand

(x^{2} - x - 3)^{2} - 2 (x^{2} - x) + 3 : x^{4} - 2 x^{3} - 7 x^{2} + 8 x + 12

x^{4} - 2 x^{3} - 7 x^{2} + 8 x + 12 = 0

Factor

x^{4} - 2 x^{3} - 7 x^{2} + 8 x + 12 : (x + 1) (x - 3) (x + 2) (x - 2)

(x + 1) (x - 3) (x + 2) (x - 2) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 1 = 0 or x - 3 = 0 or x + 2 = 0 or x - 2 = 0

Solve

x + 1 = 0 : x = - 1

Solve

x - 3 = 0 : x = 3

Solve

x + 2 = 0 : x = - 2

Solve

x - 2 = 0 : x = 2

The solutions are

x = - 1, x = 3, x = - 2, x = 2

10 = x^{10}

r^{4} + 1 = 0

16 x^{4} - 36 x^{3} + 8 x^{2} = 0

a x^{4} = 4

2 x^{3} + 4 x^{2} + 13 x + 6 = 0

What are the solutions to the equation (x^2-x-3)^2-2(x^2-x)+3=0 ?
The solutions to the equation (x^2-x-3)^2-2(x^2-x)+3=0 are x=-1,x=3,x=-2,x=2
Find the zeros of (x^2-x-3)^2-2(x^2-x)+3=0
The zeros of (x^2-x-3)^2-2(x^2-x)+3=0 are x=-1,x=3,x=-2,x=2