What are the solutions to the equation (x^2-7)^2-5(x^2-7)+6=0 ?

The solutions to the equation (x^2-7)^2-5(x^2-7)+6=0 are x=sqrt(10),x=-sqrt(10),x=3,x=-3

Find the zeros of (x^2-7)^2-5(x^2-7)+6=0

The zeros of (x^2-7)^2-5(x^2-7)+6=0 are x=sqrt(10),x=-sqrt(10),x=3,x=-3

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

x = 10, x = - 10, x = 3, x = - 3

Decimal Notation

x = 3.16227 \dots, x = - 3.16227 \dots, x = 3, x = - 3

Solution steps

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

Expand

(x^{2} - 7)^{2} - 5 (x^{2} - 7) + 6 : x^{4} - 19 x^{2} + 90

x^{4} - 19 x^{2} + 90 = 0

Rewrite the equation with

u = x^{2}

and

u^{2} = x^{4}

u^{2} - 19 u + 90 = 0

Solve

u^{2} - 19 u + 90 = 0 : u = 10, u = 9

u = 10, u = 9

Substitute back

u = x^{2},

solve for

x

Solve

x^{2} = 10 : x = 10, x = - 10

Solve

x^{2} = 9 : x = 3, x = - 3

The solutions are

x = 10, x = - 10, x = 3, x = - 3

x^{3} - 3 x^{2} + 3 x - 1

x^{4} = 12

y, x^{3} - 4 x y^{2} - 16 = 3 x - y^{4}

x^{3} - 1

r^{3} - r^{2} - r + 1 = 0

What are the solutions to the equation (x^2-7)^2-5(x^2-7)+6=0 ?
The solutions to the equation (x^2-7)^2-5(x^2-7)+6=0 are x=sqrt(10),x=-sqrt(10),x=3,x=-3
Find the zeros of (x^2-7)^2-5(x^2-7)+6=0
The zeros of (x^2-7)^2-5(x^2-7)+6=0 are x=sqrt(10),x=-sqrt(10),x=3,x=-3