X+y = 1/6 X kali y = - 1/6 Berapakah nilai x pangkat 4 + y pangkat 4?

[tex] x_{1} ^{4} + x_{2} ^{4} = ( x_{1} + x_{2})^{4} - 2 x_{1}.x_{2}=( \frac{1}{6} )^{4}-2(-\frac{1}{6})= \frac{1}{6} + 2.\frac{1}{6} =\frac{3}{6}= \frac{1}{2}[/tex]

maaf jika masih ada kekurangan

x+y = [tex] \frac{1}{6} [/tex]
x= [tex] \frac{1}{6} [/tex] - y
[tex]xy= \frac{-1}{6} [/tex]
([tex] \frac{1}{6} [/tex] - y)*y=[tex] \frac{-1}{6} [/tex]
[tex] \frac{1}{6}y- y^{2}+ \frac{1}{6}=0[/tex]
[tex] 6y^{2}-y-1=0[/tex]
[tex](2y-1)(3y+1)=0[/tex]
[tex]y= \frac{1}{2} atau y= \frac{-1}{3} [/tex]
jika y=-1/3 maka x=1/2 (berlaku sebaliknya)
[tex] x^{4} +y^{4}= (\frac{1}{2})^{4} + (\frac{-1}{3})^{4}[/tex]
                        =[tex] \frac{1}{16} + \frac{1}{81} [/tex]
                        =[tex] \frac{97}{1296} [/tex]