Решите, то, что справа заранее благодарю !

а) [latex] \left \{ {{ \frac{x}{y} + \frac{y}{x} =- \frac{5}{2} } \atop { x^{2} - y^{2} = \frac{13}{4} }} \right. [/latex] Замена [latex] \frac{x}{y} =t; \frac{y}{x} = \frac{1}{t}; x=t*y [/latex] [latex] \left \{ {{t+ \frac{1}{t} = -\frac{5}{2} } \atop {(t*y)^2-y^2=y^2*(t^2-1)= \frac{13}{4} }} \right. [/latex] 2t^2 + 2 = -5t 2t^2 + 5t + 2 = 0 (t + 2)(2t + 1) = 0 t1 = x/y = -2; x = -2y t2 = x/y = -1/2; x = -y/2 1) y^2*(t^2 - 1) = 13/4 y^2*(2^2 - 1) = 3y^2 = 13/4 y^2 = 13/12 [latex]y1=- \sqrt{ \frac{13}{12} }; x1=-2y= \sqrt{ \frac{13*4}{12} }= \sqrt{ \frac{13}{3} } [/latex] [latex]y2= \sqrt{ \frac{13}{12} }; x2=-2y=- \sqrt{ \frac{13*4}{12} }=-\sqrt{ \frac{13}{3} } [/latex] 2) y^2*(t^2 - 1) = 13/4 y^2*((1/2)^2 - 1) = -3/4*y^2 = 13/4 y^2 < 0, Решений нет б) [latex] \left \{ {{x^{2} + y^{2} = 68} \atop {\frac{x}{y} - \frac{y}{x} =\frac{17}{4} }} \right. [/latex] Замена [latex] \frac{x}{y} =t; \frac{y}{x} = \frac{1}{t}; x=t*y [/latex] [latex] \left \{ {{t- \frac{1}{t} = \frac{17}{4} } \atop {(t*y)^2+y^2=y^2*(t^2+1)= 68 }} \right. [/latex] 4t^2 - 4 = 17t 4t^2 - 17t - 4 = 0 D = 289 - 4*4(-4) = 289 + 64 = 353 1) t1 = (17 - √353)/8 = x/y [latex]t^2+1= \frac{(17- \sqrt{353})^2 }{64}+1= \frac{289+353+64-34 \sqrt{353} }{64} = \frac{353-17 \sqrt{353}}{32} [/latex] [latex]y^2*(t^2+1)=y^2*\frac{353-17 \sqrt{353}}{32}=68[/latex] [latex]y^2= \frac{68*32}{353-17 \sqrt{353}}= \frac{64*34}{353-17 \sqrt{353}} [/latex] [latex]x=t*y=(17 - \sqrt{353})/8*y[/latex] 2) t2 = (17 + √353)/8 = x/y Решается точно также в) [latex] \left \{ {{|x|+|y|=6} \atop {x^2-y^2=24}} \right. [/latex] 1) Пусть x < 0, y < 0. Тогда |x| = -x, |y| = -y [latex] \left \{ {{-x-y=6} \atop {x^2-y^2=24}} \right. [/latex] [latex] \left \{ {{x+y=-6} \atop {(x+y)(x-y)=24}} \right. [/latex] [latex] \left \{ {{x+y=-6} \atop {x-y=-4}} \right. [/latex] [latex] \left \{ {{x=-5} \atop {y=-1}} \right. [/latex] 2) Пусть x < 0, y > 0. Тогда |x| = -x, |y| = y [latex] \left \{ {{-x+y=6} \atop {x^2-y^2=24}} \right. [/latex] [latex] \left \{ {{x-y=-6} \atop {(x+y)(x-y)=24}} \right. [/latex] [latex] \left \{ {{x-y=-6} \atop {x+y=-4}} \right. [/latex] [latex] \left \{ {{x=-5} \atop {y=1}} \right. [/latex] 3) Пусть x > 0, y < 0. Тогда |x| = x, |y| = -y [latex] \left \{ {{x-y=6} \atop {x^2-y^2=24}} \right. [/latex] [latex] \left \{ {{x-y=6} \atop {(x+y)(x-y)=24}} \right. [/latex] [latex] \left \{ {{x-y=6} \atop {x+y=4}} \right. [/latex] [latex] \left \{ {{x=5} \atop {y=-1}} \right. [/latex] 4) Пусть x > 0, y > 0. Тогда |x| = x, |y| = y [latex] \left \{ {{x+y=6} \atop {x^2-y^2=24}} \right. [/latex] [latex] \left \{ {{x+y=6} \atop {(x+y)(x-y)=24}} \right. [/latex] [latex] \left \{ {{x+y=6} \atop {x-y=4}} \right. [/latex] [latex] \left \{ {{x=5} \atop {y=1}} \right. [/latex] г) [latex] \left \{ {{|x|-|y|=4} \atop {x^2+y^2=41}} \right. [/latex] 1) Пусть x < 0, y < 0. Тогда |x| = -x, |y| = -y [latex] \left \{ {{-x+y=4} \atop {x^2+y^2=41}} \right. [/latex] [latex] \left \{ {{x^2-2xy+y^2=16} \atop {x^2+y^2=41}} \right. [/latex] Подставляем 2 ур-ние в 1 ур-ние [latex]41-2xy=16[/latex] [latex]xy= \frac{41-16}{2}= \frac{25}{2} =12,5 [/latex] [latex] \left \{ {{x-y=-4} \atop {xy=12,5}} \right. [/latex] [latex] \left \{ {{x=y-4} \atop {y(y-4)=12,5}} \right. [/latex] y^2 - 4y - 12,5 = 0 2y^2 - 8y - 25 = 0 D/4 = 4^2 - 2*(-25) = 16 + 50 = 66 = (√66)^2 y1 = (4-√66)/2; x1 = y-4 = (-4-√66)/2 y2 = (4+√66)/2; x2 = y-4 = (-4+√66)/2 2) Пусть x < 0, y > 0. Тогда |x| = -x, |y| = y [latex] \left \{ {{-x-y=4} \atop {x^2+y^2=41}} \right. [/latex] [latex] \left \{ {{x^2+2xy+y^2=16} \atop {x^2+y^2=41}} \right. [/latex] Подставляем 2 ур-ние в 1 ур-ние [latex]41+2xy=16[/latex] [latex]xy= \frac{-41+16}{2}= \frac{-25}{2} =-12,5 [/latex] [latex] \left \{ {{x+y=-4} \atop {xy=-12,5}} \right. [/latex] [latex] \left \{ {{x=-y-4} \atop {y(-y-4)=-12,5}} \right. [/latex] -y^2 - 4y + 12,5 = 0 2y^2 + 8y - 25 = 0 D/4 = 16 + 2*25 = 16 + 50 = 66 = (√66)^2 y3 = (-4-√66)/2; x3 = -y-4 = (-4+√66)/2 y4 = (-4+√66)/2; x4 = -y-4 = (-4-√66)/2 3) Пусть x > 0, y < 0. Тогда |x| = x, |y| = -y [latex] \left \{ {{x+y=4} \atop {x^2+y^2=41}} \right. [/latex] [latex] \left \{ {{x^2+2xy+y^2=16} \atop {x^2+y^2=41}} \right. [/latex] Подставляем 2 ур-ние в 1 ур-ние [latex]41+2xy=16[/latex] [latex]xy= \frac{-41+16}{2}= \frac{-25}{2} =-12,5 [/latex] [latex] \left \{ {{x+y=4} \atop {xy=-12,5}} \right. [/latex] [latex] \left \{ {{x=-y+4} \atop {y(-y+4)=-12,5}} \right. [/latex] -y^2 + 4y + 12,5 = 0 2y^2 - 8y - 25 = 0 D/4 = 4^2 - 2*(-25) = 16 + 50 = 66 = (√66)^2 y5 = (4-√66)/2; x5 = -y+4 = (4+√66)/2 y6 = (4+√66)/2; x6 = -y+4 = (4-√66)/2 4) Пусть x > 0, y > 0. Тогда |x| = x, |y| = y [latex] \left \{ {{x-y=4} \atop {x^2+y^2=41}} \right. [/latex] [latex] \left \{ {{x^2-2xy+y^2=16} \atop {x^2+y^2=41}} \right. [/latex] Подставляем 2 ур-ние в 1 ур-ние [latex]41-2xy=16[/latex] [latex]xy= \frac{41-16}{2}= \frac{25}{2} =12,5 [/latex] [latex] \left \{ {{x-y=4} \atop {xy=12,5}} \right. [/latex] [latex] \left \{ {{x=y+4} \atop {y(y+4)=12,5}} \right. [/latex] y^2 + 4y - 12,5 = 0 2y^2 + 8y - 25 = 0 D/4 = 4^2 - 2*(-25) = 16 + 50 = 66 = (√66)^2 y7 = (-4-√66)/2; x7 = y+4 = (4-√66)/2 y8 = (-4+√66)/2; x8 = y+4 = (4+√66)/2