Question

решите ленейное уравнение ​

Answer 1

Ответ:

$(4+4\sqrt{2} \ ; \ -4+4\sqrt{2}) \ ; \ (4-4\sqrt{2} \ ; \ -4-4\sqrt{2}) \ ;$

Объяснение:

$\displaystyle \left \{ {{x^{2}+y^{2}=96} \atop {x-y=8}} \right. \Rightarrow \left \{ {{x=y+8} \atop {(y+8)^{2}+y^{2}=96}} \right. \Rightarrow \left \{ {{x=y+8} \atop {y^{2}+16y+64+y^{2}-96=0}} \right. \Leftrightarrow$

$\displaystyle \Leftrightarrow \left \{ {{x=y+8} \atop {2y^{2}+16y-32=0}} \right. \Leftrightarrow \left \{ {{x=y+8} \atop {y^{2}+8y-16=0}} \right. ;$

$y^{2}+8y-16=0;$

$D=b^{2}-4ac \Rightarrow D=8^{2}-4 \cdot 1 \cdot (-16)=64+64=128;$

$y_{1,2}=\dfrac{-b \pm \sqrt{D}}{2a} \Rightarrow y_{1,2}=\dfrac{-8 \pm \sqrt{128}}{2 \cdot 1}=\dfrac{-8 \pm 8\sqrt{2}}{2}=-4 \pm 4\sqrt{2} \ ;$

$y_{1,2}=-4 \pm 4\sqrt{2} \Rightarrow x_{1,2}=-4 \pm 4\sqrt{2}+8=4 \pm 4\sqrt{2} \ ;$

$(4+4\sqrt{2} \ ; \ -4+4\sqrt{2}) \ ; \ (4-4\sqrt{2} \ ; \ -4-4\sqrt{2}) \ ;$