Вопрос пользователя:
Записать формулу корней квадратного уравнения х²+2mх+с=0, решить с помощью этой формулы уравнение:
1. х²+10х+24=0
2. х²-23х-51=0
Илюха отвечает:
sqrt{m^2-c}-m" title="x_1=frac{-2m+sqrt{(2m)^2-4c}}{2}=frac{-2m+sqrt{4m^2-4c}}{2}=frac{-2m+sqrt{4(m^2-c)}}{2}=frac{-2m+2sqrt{m^2-c}}{2}=-m+sqrt{m^2-c}=sqrt{m^2-c}-m" alt="x_1=frac{-2m+sqrt{(2m)^2-4c}}{2}=frac{-2m+sqrt{4m^2-4c}}{2}=frac{-2m+sqrt{4(m^2-c)}}{2}=frac{-2m+2sqrt{m^2-c}}{2}=-m+sqrt{m^2-c}=sqrt{m^2-c}-m" />
sqrt{m^2-c})[/tex]
1) x^2+10x+24=0" title="x_2=frac{-2m-sqrt{(2m)^2-4c}}{2}=frac{-2m-sqrt{4m^2-4c}}{2}=frac{-2m-sqrt{4(m^2-c)}}{2}=frac{-2m-2sqrt{m^2-c}}{2}=-m-sqrt{m^2-c}=-(m+sqrt{m^2-c})" title="x^2+10x+24=0" title="x_2=frac{-2m-sqrt{(2m)^2-4c}}{2}=frac{-2m-sqrt{4m^2-4c}}{2}=frac{-2m-sqrt{4(m^2-c)}}{2}=frac{-2m-2sqrt{m^2-c}}{2}=-m-sqrt{m^2-c}=-(m+sqrt{m^2-c})" alt="x^2+10x+24=0" title="x_2=frac{-2m-sqrt{(2m)^2-4c}}{2}=frac{-2m-sqrt{4m^2-4c}}{2}=frac{-2m-sqrt{4(m^2-c)}}{2}=frac{-2m-2sqrt{m^2-c}}{2}=-m-sqrt{m^2-c}=-(m+sqrt{m^2-c})" />
1) x^2+10x+24=0" alt="x_2=frac{-2m-sqrt{(2m)^2-4c}}{2}=frac{-2m-sqrt{4m^2-4c}}{2}=frac{-2m-sqrt{4(m^2-c)}}{2}=frac{-2m-2sqrt{m^2-c}}{2}=-m-sqrt{m^2-c}=-(m+sqrt{m^2-c})" title="x^2+10x+24=0" alt="x_2=frac{-2m-sqrt{(2m)^2-4c}}{2}=frac{-2m-sqrt{4m^2-4c}}{2}=frac{-2m-sqrt{4(m^2-c)}}{2}=frac{-2m-2sqrt{m^2-c}}{2}=-m-sqrt{m^2-c}=-(m+sqrt{m^2-c})" alt="x^2+10x+24=0" alt="x_2=frac{-2m-sqrt{(2m)^2-4c}}{2}=frac{-2m-sqrt{4m^2-4c}}{2}=frac{-2m-sqrt{4(m^2-c)}}{2}=frac{-2m-2sqrt{m^2-c}}{2}=-m-sqrt{m^2-c}=-(m+sqrt{m^2-c})" />
1) x^2+10x+24=0" />
sqrt{m^2-c}-m" title="x_1=sqrt{m^2-c}-m" alt="x_1=sqrt{m^2-c}-m" />
sqrt{5^2-24}-5=1-5=-4" title="x^2+10x+24=0" />
sqrt{m^2-c}-m" title="x_1=sqrt{m^2-c}-m" alt="x_1=sqrt{m^2-c}-m" />
sqrt{5^2-24}-5=1-5=-4" alt="x^2+10x+24=0" />
sqrt{m^2-c}-m" title="x_1=sqrt{m^2-c}-m" alt="x_1=sqrt{m^2-c}-m" />
sqrt{5^2-24}-5=1-5=-4" />
x_2=-(m+sqrt{m^2-c})" title="x_1=sqrt{5^2-24}-5=1-5=-4" title="x_2=-(m+sqrt{m^2-c})" title="x_1=sqrt{5^2-24}-5=1-5=-4" alt="x_2=-(m+sqrt{m^2-c})" title="x_1=sqrt{5^2-24}-5=1-5=-4" />
x_2=-(m+sqrt{m^2-c})" alt="x_1=sqrt{5^2-24}-5=1-5=-4" title="x_2=-(m+sqrt{m^2-c})" alt="x_1=sqrt{5^2-24}-5=1-5=-4" alt="x_2=-(m+sqrt{m^2-c})" alt="x_1=sqrt{5^2-24}-5=1-5=-4" />
x_2=-(m+sqrt{m^2-c})" />
-(5+sqrt{5^2-24})=-(5+1)=-6" title="x_2=-(m+sqrt{m^2-c})" />
-(5+sqrt{5^2-24})=-(5+1)=-6" alt="x_2=-(m+sqrt{m^2-c})" />
-(5+sqrt{5^2-24})=-(5+1)=-6" />
Ответ: -6; -4.
2) x^2-23x-51=0" title="x_2=-(5+sqrt{5^2-24})=-(5+1)=-6" title="x^2-23x-51=0" title="x_2=-(5+sqrt{5^2-24})=-(5+1)=-6" alt="x^2-23x-51=0" title="x_2=-(5+sqrt{5^2-24})=-(5+1)=-6" />
Ответ: -6; -4.
2) x^2-23x-51=0" alt="x_2=-(5+sqrt{5^2-24})=-(5+1)=-6" title="x^2-23x-51=0" alt="x_2=-(5+sqrt{5^2-24})=-(5+1)=-6" alt="x^2-23x-51=0" alt="x_2=-(5+sqrt{5^2-24})=-(5+1)=-6" />
Ответ: -6; -4.
2) x^2-23x-51=0" />
sqrt{m^2-c}-m" title="x_1=sqrt{m^2-c}-m" alt="x_1=sqrt{m^2-c}-m" />
sqrt{(-11,5)^2-(-51)}-(-11,5)=11,5+sqrt{frac{733}{4}}=11,5+0,5sqrt{733}" title="x^2-23x-51=0" />
sqrt{m^2-c}-m" title="x_1=sqrt{m^2-c}-m" alt="x_1=sqrt{m^2-c}-m" />
sqrt{(-11,5)^2-(-51)}-(-11,5)=11,5+sqrt{frac{733}{4}}=11,5+0,5sqrt{733}" alt="x^2-23x-51=0" />
sqrt{m^2-c}-m" title="x_1=sqrt{m^2-c}-m" alt="x_1=sqrt{m^2-c}-m" />
sqrt{(-11,5)^2-(-51)}-(-11,5)=11,5+sqrt{frac{733}{4}}=11,5+0,5sqrt{733}" />
x_2=-(m+sqrt{m^2-c})" title="x_1=sqrt{(-11,5)^2-(-51)}-(-11,5)=11,5+sqrt{frac{733}{4}}=11,5+0,5sqrt{733}" title="x_2=-(m+sqrt{m^2-c})" title="x_1=sqrt{(-11,5)^2-(-51)}-(-11,5)=11,5+sqrt{frac{733}{4}}=11,5+0,5sqrt{733}" alt="x_2=-(m+sqrt{m^2-c})" title="x_1=sqrt{(-11,5)^2-(-51)}-(-11,5)=11,5+sqrt{frac{733}{4}}=11,5+0,5sqrt{733}" />
x_2=-(m+sqrt{m^2-c})" alt="x_1=sqrt{(-11,5)^2-(-51)}-(-11,5)=11,5+sqrt{frac{733}{4}}=11,5+0,5sqrt{733}" title="x_2=-(m+sqrt{m^2-c})" alt="x_1=sqrt{(-11,5)^2-(-51)}-(-11,5)=11,5+sqrt{frac{733}{4}}=11,5+0,5sqrt{733}" alt="x_2=-(m+sqrt{m^2-c})" alt="x_1=sqrt{(-11,5)^2-(-51)}-(-11,5)=11,5+sqrt{frac{733}{4}}=11,5+0,5sqrt{733}" />
x_2=-(m+sqrt{m^2-c})" />
[tex]x_2=-(-11,5+sqrt{(-11,5)^2-(-51)})=11,5-sqrt{frac{733}{4}}=11,5-0,5sqrt{733}" title="x_2=-(m+sqrt{m^2-c})" />
[tex]x_2=-(-11,5+sqrt{(-11,5)^2-(-51)})=11,5-sqrt{frac{733}{4}}=11,5-0,5sqrt{733}" alt="x_2=-(m+sqrt{m^2-c})" />
[tex]x_2=-(-11,5+sqrt{(-11,5)^2-(-51)})=11,5-sqrt{frac{733}{4}}=11,5-0,5sqrt{733}" />
Ответ: x_1=11,5+0,5sqrt{733}" title="x_1=11,5+0,5sqrt{733}" alt="x_1=11,5+0,5sqrt{733}" />; x_2=11,5-0,5sqrt{733}" title="x_2=11,5-0,5sqrt{733}" alt="x_2=11,5-0,5sqrt{733}" />.