Question #22486

Solve the given equations by factoring.
8a. a^8=9a^6
8b. x^3-5x^2-4x+20=0

Expert's answer

8a. a^8=9a^6

a^8-9a^6=0

a^6(a^2-9)=0

a^6=0 or a^2-9=0

From first equation a=0 and from second equation a=3 or a=-3

Answer: a = -3, 0, 3

8b. x^3-5x^2-4x+20=0

We grouped x^3 with -4x and -5x^2 with 20

Then we have:

(x^3-4x)-(5x^2-20)=0

x(x^2-4)-5(x^2-4)=0

(x^2-4)(x-5)=0

Then x^2-4=0 or x-5=0

x=-2, 2 or x=0

Answer: x=-2, 0, 2

a^8-9a^6=0

a^6(a^2-9)=0

a^6=0 or a^2-9=0

From first equation a=0 and from second equation a=3 or a=-3

Answer: a = -3, 0, 3

8b. x^3-5x^2-4x+20=0

We grouped x^3 with -4x and -5x^2 with 20

Then we have:

(x^3-4x)-(5x^2-20)=0

x(x^2-4)-5(x^2-4)=0

(x^2-4)(x-5)=0

Then x^2-4=0 or x-5=0

x=-2, 2 or x=0

Answer: x=-2, 0, 2

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