решите систему неравенств x^2+2x-3>=0 x^2+16x-3>=0 x+3<=1
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sedinalanax^2+2x-3>=0⇒(x+3)(x-1)≥0⇒x≤-3 U x≥1 x^2+16x-3>=0⇒(x+8+√67)(x+8-√76)≥0⇒x≤-8-√67 U x≥-8+√67 x+3<=1⇒x≤-2 x²+2x-3=0 x1+x2=-2 U x1*x2=-3⇒x1=-3 U x2=1 x²+16x-3=0 D=256+12=268 x1=(-16-2√67)/2=-8-√67 U x2=-8+√67 \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ -------[-8-√67]------------[-3]-----------[-2]----------[-8+√67]------------[1]-------- \\\\\\\\\\\\\\\ ///////////////////////////////////// ///////////////////////////////////// \\\\\\\\\\\\\\\\\ x∈(-∞;-8-√67]
Answers & Comments
x^2+16x-3>=0⇒(x+8+√67)(x+8-√76)≥0⇒x≤-8-√67 U x≥-8+√67
x+3<=1⇒x≤-2
x²+2x-3=0
x1+x2=-2 U x1*x2=-3⇒x1=-3 U x2=1
x²+16x-3=0
D=256+12=268
x1=(-16-2√67)/2=-8-√67 U x2=-8+√67
\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
-------[-8-√67]------------[-3]-----------[-2]----------[-8+√67]------------[1]--------
\\\\\\\\\\\\\\\ /////////////////////////////////////
///////////////////////////////////// \\\\\\\\\\\\\\\\\
x∈(-∞;-8-√67]