# Answer to Question #22216 in Algebra for Brenden Fields

Question #22216

Solve each quadratic in form equation.

9. x^4-8x^2+7=0

10. x^4-2x^2-35=0

9. x^4-8x^2+7=0

10. x^4-2x^2-35=0

Expert's answer

9.& x^4-8x^2+7=0

x^2=y

y^2-8y+7=0

D=64-4*7*1=36

y=(8+6)/2= 7

y=(8-6)/2=1

x1= sqrt(7)

x2=-sqrt(7)

x3=1

x4=-1

10. x^4-2x^2-35=0

x^2=y

y^2-2y-35=0

D=4+4*35*1=144

y=(2+12)/2= 7

y=(2-12)/2=irrational roots

x1= sqrt(7)

x2=-sqrt(7)

x^2=y

y^2-8y+7=0

D=64-4*7*1=36

y=(8+6)/2= 7

y=(8-6)/2=1

x1= sqrt(7)

x2=-sqrt(7)

x3=1

x4=-1

10. x^4-2x^2-35=0

x^2=y

y^2-2y-35=0

D=4+4*35*1=144

y=(2+12)/2= 7

y=(2-12)/2=irrational roots

x1= sqrt(7)

x2=-sqrt(7)

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