203 204 срочно заранее спасибо.

Question 1

Question 2

Решите задачу:

$203)\; \; \left \{ {{2^{x}\cdot 4^{y^2}=256} \atop {lnx+2\, lny=ln(lg10^8)}} \right. \; \; \left \{ {{2^{x}\cdot 2^{2y^2}=2^8} \atop {lnx+lny^2=ln8}} \right. \; \; \left \{ {{x+2y^2=8} \atop {x\cdot y^2=8}} \right. \\\\ \left \{ {{\frac{8}{y^2}+2y^2-8=0} \atop {x=8/y^2}} \right. \; \left \{ {{8+2y^4-8y^2=0} \atop {x=8/y^2}} \right. \\\\2y^4-8y^2+8=0\; ,\; \; y^4-4y^2+4=0\; ,\; \; (y^2-2)^2=0\; \; \to \\\\y^2-2=0\; \; \to \; \; y=\pm \sqrt2\\\\x=\frac{8}{y^2}=\frac{8}{2}=4$

$ODZ:\; \; x\ \textgreater \ 0\; ,\; y\ \textgreater \ 0\; \; \to \; \; \; x=4\; y=\sqrt2\\\\x+y=4+\sqrt2\; .$

$204)\; \; \left \{ {{9^{x^2}\cdot 3^{y}=729} \atop {2\, lnx+lny=ln(\frac{3}{2}lg1000)}} \right. \; \; \left \{ {{3^{2x^2}\cdot 3^{y}=3^6} \atop {lnx^2+lny=ln(\frac{3}{2}lg10^3)}} \right. \; \; \left \{ {{3^{2x^2+y}=3^6} \atop {ln(y\cdot x^2)=ln(\frac{3}{2}\cdot 3)}} \right. \\\\ \left \{ {{2x^2+y=6} \atop {y\cdot x^2=\frac{9}{2}}} \right. \; \; \left \{ {{2x^2+\frac{9}{2x^2}=6} \atop {y=\frac{9}{2x^2}}} \right. \; \; \left \{ {{4x^4-12x^2+9=0} \atop {y=\frac{9}{2x^2}}} \right.$

$(2x^2)^2-12x^2+9=0,\; \; (2x^2-3)^2=0\; ,\; \; 2x^2-3=0$

$x^{2} = \frac{3}{2} \; \; \to \; \; \; x=\pm \sqrt{\frac{3}{2}}\\\\y=\frac{9}{2x^2}= \frac{9}{2\cdot 3/2} = 3\\\\ODZ:\; \; x\ \textgreater \ 0\; ,\; y\ \textgreater \ 0\; \; \to \; \; x=\sqrt{\frac{3}{2}}\; ,\; \underline {y=3}\; .$