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

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