Решите систему уравнений {(5x+3)²=8y,(3x+5)²=8y.  

[latex] left { {{(5x+3)^{2}=8y} atop {(3x+5)^{2}=8y}} ight. left { {{(5x+3)^{2}=(3x+5)^{2}} atop {8y=9x^{2}+30x+25}} ight. left { {{x=1} atop {8y=64}} ight. left { {{x=1} atop {y=8}} ight. [/latex][latex](5x+3)^{2}=(3x+5)^{2}[/latex][latex]25x^{2}+30x+9=9x^{2}+30x+25[/latex][latex]25x^{2}-9x^{2}=25-9[/latex][latex]16x^{2}=16[/latex][latex]x^{2}=16:16[/latex][latex]x^{2}=1[/latex][latex]x=1[/latex]