Answer:
[tex]x=+10i,-10i,\sqrt{5} ,-\sqrt{5}[/tex]
Step-by-step explanation:
[tex]x^4 + 95x^2 -500 = 0[/tex]
REwrite the equation in the form of quadratic equation ax^2+bx+c=0
To solve for x , we replace x^2 by 'u'
[tex]u^2 + 95u -500 = 0[/tex]
Now we factor the left hand side
Product is -500 and sum is 95
100 times -5 is -500
100 + (-5) is 95, factors are 100 and -5
[tex]u^2 + 95u -500 = 0[/tex]
[tex](u+100)(u-5) = 0[/tex]
Replace u with x^2
[tex](x^2+100)(x^2-5) = 0[/tex]
Set each factor =0 and solve for x
[tex]x^2+100= 0, x^2=-100[/tex]
[tex]x^2-5= 0, x^2=5[/tex]
To remove square , take square root on both sides
square root (-1) is 'i'
[tex]x^2=-100, x= +-10i[/tex]
[tex]x^2=5, x=+-\sqrt{5}[/tex]
