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What are the solutions of the equation x4 + 95x2 – 500 = 0? Use factoring to solve.


x=+- sqrt 5 and x = ±10
x=+- sqrt i5 and x = ±10i
x=+- sqrt 5 and x = ±10i
x=+- sqrt i5 and x = ±10

Respuesta :

x= the square root of 5
x= the square root of -5
x=10i
x=-10i

Given

The equation in the form

[tex]x^{4}+95x^{2}-500 =0[/tex]

Find the factor of the above equation

To proof

factoring the above equation

we get

[tex]x^{4}+100x^{2}-5x^{2}-500 =0\\\\x^{2}(x^{2}+100)-5(x^{2}+100)=0\\\\(x^{2}-5)(x^{2}+100)=0[/tex]

now sloving the equation we get the value

x² = 5

x² = -100

[tex]x =\pm \sqrt{5}\\\\ x=\sqrt{-100}[/tex]

The factor of the equation is

[tex]x=\pm \sqrt{5}\\\\ x= \pm 10i[/tex]

Hence proved