What are the solutions to the equation a^4-10a^2=-21 ?

The solutions to the equation a^4-10a^2=-21 are a=sqrt(7),a=-sqrt(7),a=sqrt(3),a=-sqrt(3)

Find the zeros of a^4-10a^2=-21

The zeros of a^4-10a^2=-21 are a=sqrt(7),a=-sqrt(7),a=sqrt(3),a=-sqrt(3)

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a^{4} - 10 a^{2} = - 21

a = 7, a = - 7, a = 3, a = - 3

Decimal Notation

a = 2.64575 \dots, a = - 2.64575 \dots, a = 1.73205 \dots, a = - 1.73205 \dots

Solution steps

a^{4} - 10 a^{2} = - 21

Move

21

to the left side

a^{4} - 10 a^{2} + 21 = 0

Rewrite the equation with

u = a^{2}

and

u^{2} = a^{4}

u^{2} - 10 u + 21 = 0

Solve

u^{2} - 10 u + 21 = 0 : u = 7, u = 3

u = 7, u = 3

Substitute back

u = a^{2},

solve for

a

Solve

a^{2} = 7 : a = 7, a = - 7

Solve

a^{2} = 3 : a = 3, a = - 3

The solutions are

a = 7, a = - 7, a = 3, a = - 3

a^{3} = - 8

x^{3} + 5 = 26

(x - 3) (x + 5) (x - 7) (x + 1) = 0

y^{4} y + 1 = 13

2 x^{3} + 7 = 25

What are the solutions to the equation a^4-10a^2=-21 ?
The solutions to the equation a^4-10a^2=-21 are a=sqrt(7),a=-sqrt(7),a=sqrt(3),a=-sqrt(3)
Find the zeros of a^4-10a^2=-21
The zeros of a^4-10a^2=-21 are a=sqrt(7),a=-sqrt(7),a=sqrt(3),a=-sqrt(3)