Question

Rezolvati ecuatia:
$\sqrt{2( x^{4}-16)} = x^{2}+12$

Answer 1

     
$\sqrt{2( x^{4}-16)} = x^{2}+12 \,\,\, ridicam \,\,\, la \,\,\,patrat \\ 2( x^{4}-16)= (x^{2}+12)^{2} \\ 2 x^{4}-32= x^{4}+24 x^{2} +144 \\ 2 x^{4}-32- x^{4}-24 x^{2} -144=0 \\ x^{4}-24 x^{2} -176=0 \\ y= x^{2} \\ y^{2}-24y-176 \\ \\ y1= \frac{24+ \sqrt{24^{2}+4*176} }{2}=\frac{24+ \sqrt{576+704}}{2}= \frac{24+ \sqrt{1280}}{2}=\frac{24+ 16\sqrt{5}}{2}= 12+8\sqrt{5} \\ y2=12-8\sqrt{5} \\ y2 <0 \,\,\, se \,\,\, exclude \\ x= \sqrt{y1}=+/- \sqrt{12+8\sqrt{5}}$