Question

203 204 срочно заранее спасибо.

Answer 1

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

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

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

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

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