Алгебра 8 класс учебник Макарычев, Миндюк ответы – номер 705

а) $$ \left\{\begin{array} { l } { x + y = 8 } \\ { x y = - 2 0 } \end{array} \left\{\begin{array} { l } { y = 8 - x } \\ { x ( 8 - x ) = - 2 0 } \end{array} \left\{\begin{array}{l} y=8-x \\ -x^2+8 x+20=0 \end{array}\right.\right.\right. $$
−х² + 8х + 20 = 0 D = b² − 4ac = 8² − 4 ⋅ (−1) ⋅ 20 = 64 + 80 = 144 > 0, имеет 2 корня
x₁ = $$ \frac{-b+\sqrt{D}}{2 a}=\frac{-8+\sqrt{144}}{2(-1)} $$ = −8 + 12/−2 = 4/−2 = −2 x₂ = $$ \frac{-b-\sqrt{D}}{2 a}=\frac{-8-\sqrt{144}}{2(-1)}= $$ = −8 − 12/−2 = −20/−2 = 10
x₁ = −2, x₂ = 10
$$ \left\{\begin{array} { l } { x _ { 1 } = - 2 } \\ { y _ { 1 } = 8 + 2 = 1 0 } \end{array} \left\{\begin{array}{l} x_1=-2 \\ y_1=10 \end{array}\right.\right. $$
$$ \left\{\begin{array} { l } { x _ { 2 } = 1 0 } \\ { y _ { 2 } = 8 - 1 0 = - 2 } \end{array} \left\{\begin{array}{l} x_2=10 \\ y_2=-2 \end{array}\right.\right. $$
(−2; 10), (10; −2)
б) $$ \left\{\begin{array} { l } { x - y = 0 , 8 } \\ { x y = 2 , 4 } \end{array} \left\{\begin{array} { l } { y = x - 0 , 8 } \\ { x ( x - 0 , 8 ) = 2 , 4 } \end{array} \left\{\begin{array}{l} y=x-0,8 \\ x^2-0,8 x-2,4=0 \end{array}\right.\right.\right. $$
х² − 0,8х − 2,4 = 0 D = b² − 4ac = (−0,8)² − 4 ⋅ 1 ⋅ (−2,4) = 0,64 + 9,6 = 10,24 > 0, имеет 2 корня
x₁ = $$ \frac{-b+\sqrt{D}}{2 a}=\frac{0,8+\sqrt{10,24}}{2 ⋅ 1} $$ = 0,8 + 3,2/2 = 4/2 = 2 x₂ = $$ \frac{-b-\sqrt{D}}{2 a}=\frac{0,8-\sqrt{10,24}}{2 ⋅ 1} $$ = 0,8 − 3,2/2 = −2,4/2 = −1,2
x₁ = 2, x₂ = −1,2
$$ \left\{\begin{array} { l } { x _ { 1 } = 2 } \\ { y _ { 1 } = 2 - 0 , 8 = 1 , 2 } \end{array} \left\{\begin{array}{l} x_1=2 \\ y_1=1,2 \end{array}\right.\right. $$
$$ \left\{\begin{array} { l } { x _ { 2 } = - 1 , 2 } \\ { y _ { 2 } = - 1 , 2 - 0 , 8 = - 2 } \end{array} \left\{\begin{array}{l} x_2=-1,2 \\ y_2=-2 \end{array}\right.\right. $$
(2; 1,2), (−1,2; −2)
в) $$ \left\{\begin{array} { l } { x ^ { 2 } - y ^ { 2 } = 8 } \\ { x - y = 4 } \end{array} \left\{\begin{array}{l} x^2-(x-4)^2=8 \\ y=x-4 \end{array}\right.\right. $$ $$ \left\{\begin{array}{l} x^2-x^2+8 x-16-8=0\left\{\begin{array}{l} 8 x-24=0 \\ y=x-4 \end{array}\right. \\ y=x-4 \end{array}\right. $$
$$ \left\{\begin{array} { l } { 8 x = 2 4 } \\ { y = x - 4 } \end{array} \left\{\begin{array} { l } { x = 2 4 \div 8 } \\ { y = x - 4 } \end{array} \left\{\begin{array} { l } { x = 3 } \\ { y = 3 - 4 = - 1 } \end{array} \left\{\begin{array}{l} x=3 \\ y=-1 \end{array}\right.\right.\right.\right. $$
(3; −1)
г) $$ \left\{\begin{array} { l } { x ^ { 2 } + y ^ { 2 } = 5 } \\ { x + y = - 3 } \end{array} \left\{\begin{array}{l} x^2+(-x-3)^2=5 \\ y=-x-3 \end{array}\right.\right. $$ $$ \left\{\begin{array} { l } { x ^ { 2 } + x ^ { 2 } + 6 x + 9 - 5 = 0 } \\ { y = - x - 3 } \end{array} \left\{\begin{array}{l} 2 x^2+6 x+4=0 \\ y=-x-3 \end{array}\right.\right. $$
2х² + 6х + 4 = 0 D = b² − 4ac = 6² − 4 ⋅ 2 ⋅ 4 = 36 − 32 = 4 > 0, имеет 2 корня
x₁ = $$ \frac{-b+\sqrt{D}}{2 a}=\frac{-6+\sqrt{4}}{2 ⋅ 2} $$ = −6 + 2/4 = −4/2 = −1 x₂ = $$ \frac{-b-\sqrt{D}}{2 a}=\frac{-6-\sqrt{4}}{2 ⋅ 2} $$ = −6 − 2/4 = −8/2 = −2
x₁ = −1, x₂ = −2
$$ \left\{\begin{array} { l } { x _ { 1 } = - 1 } \\ { y _ { 1 } = 1 - 3 = - 2 } \end{array} \left\{\begin{array}{l} x_1=-1 \\ y_1=-2 \end{array}\right.\right. $$
$$ \left\{\begin{array} { l } { x _ { 2 } = - 2 } \\ { y _ { 2 } = 2 - 3 = - 1 } \end{array} \left\{\begin{array}{l} x_2=-2 \\ y_2=-1 \end{array}\right.\right. $$
(−1; −2), (−2; −1)