Question

3 номер срочнооооо, плиссссс

Answer 1

$left { {{2^{x+y-1}=1} atop {3^{xy}=(frac{1}{3}})^{sqrt2}} right. ; left { {{2^{x+y-1}=2^0} atop {3^{xy}=3^{-sqrt2}}} right. ; left { {{x+y-1=0 atop {xy=-sqrt2}} right. ; left { {{y=1-x} atop {x(1-x)=-sqrt2}} right. \\x(1-x)=x-x^2\\x-x^2=-sqrt2\\x^2-x-sqrt2=0\\D=1+4sqrt2\\x_1= frac{1-sqrt{1+4sqrt2}}{2} ; ,; ; x_2=frac{1+sqrt{1+4sqrt2}}{2}\\y_1=1- frac{1-sqrt{1+4sqrt2}}{2}= frac{1+sqrt{1+4sqrt2}}{2} ; ,$

$y_2=1- frac{1+sqrt{1+4sqrt2}}{2}=frac{1-sqrt{1+4sqrt2}}{2}$

$x_1^2+y_1^2=x_2^2+y_2^2= frac{(1-sqrt{1+4sqrt2})^2}{4} + frac{(1+sqrt{1+4sqrt2})^2}{4} =\\= frac{(1-2sqrt{1+4sqrt2}+, 1+4sqrt2)+(1+2sqrt{1+4sqrt2}+, 1+4sqrt2)}{4} =\\= frac{4+8sqrt2}{4} = frac{4(1+2sqrt2)}{4} =1+2sqrt2$