`sin^4x+cos^4(x+π/4)=1/4`
`<=>((1-cos2x)/2)^2+(1+cos(2x+π/2)/2)^2=1/4`
`<=>(1-cos2x)^2+((1+cos(2x+π))/2)^2=1`
`<=>cos^2 2x-2cos2x+1+cos^2(2x+π/2)+2cos(2x+π/2)+1=1`
`<=>cos^2 2x+2cos2x+sin^2 2x-2sin2x+1=0`
`<=>2-2(sin2x+cos2x)=0`
`<=>sin2x+cos2x=1`
`<=>sqrt(2)sin(2x+π/4)=1`
`<=>`\(\left[ \begin{array}{l}x=kπ\\x=\dfrac{π}{4}+kπ\end{array} \right.\)
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