14 балла номер 161-163

[latex] \frac{(181^2-61^2)}{(319^2-209^2)} = \frac{(181-61)(181+61)}{(319-209)(319+209)} = \frac{20*242}{110*519} = \frac{2*10*11*11}{11*10*173*3}= \frac{22}{519} [/latex] [latex] \frac{(38^2-17^2)}{(47^2-19^2)}= \frac{(38-17)(38+17)}{(47-19)(47+19)} = \frac{21*55}{28*66}= \frac{1155}{1848} =0.625 [/latex] [latex](m+5)^2-(m-5)^2=(m^2+10m+25)-(m^2-10m+25)=20m[/latex] [latex](x+y)^2-(x-y)^2=(x^2+2xy+y^2)-(x^2-2xy+y^2)=4xy[/latex] [latex](x-6)^2-9x^2=(x^2-12x+36)-9x^2=-8x^2-12x+36[/latex] [latex](6-n)^2-(n+6)^2=(36-12n+n^2)-(n^2+12n+36)=-24n[/latex] [latex](2p-q)^2-(q+2p)^2=(4p^2-4pq+q^2)-(q^2+4pq+4p^2)=-8pq[/latex] [latex]4y^2-(y+3)^2=4y^2-(y^2+6y+9)=3y^2-6y-9[/latex] [latex]81x^2-9=0[/latex] [latex]9(9x^2-1)=0[/latex] [latex]9x^2-1=0[/latex] [latex]9x^2=1[/latex] [latex]x^2= \frac{1}{9} [/latex] [latex]|x= \sqrt{ \frac{1}{9} } [/latex] [latex]|x= \frac{1}{3} [/latex] [latex]|x=- \sqrt{ \frac{1}{9} } [/latex] [latex]|x=- \frac{1}{3} [/latex] Ответ:[latex] \frac{1}{3} ;- \frac{1}{3} [/latex] [latex]-4y^2+16=0\\ 4y^2-16=0\\ 4(y^2-4)=0\\ y^2=4\\ |y= \sqrt{4} |y=2\\ |y= -\sqrt{4}|y=-2 [/latex] Ответ: [latex]2;-2[/latex]