x2+x-15=0 x2-45x-50=02x2-2x-80=0 решить через дискриминант.. Created by mejaj11838. algebra-ru

x2+x-15=0 x2-45x-50=02x2-2x-80=0 решить через дискриминант...

Avantgardе

Ответ:

$1)\ \ x^2+x-15=0\\\\D=b^2-4ac=1+60=61\ \ ,\ \ \ \ x_{1,2}=\dfrac{-b\pm \sqrt{D}}{2a}\\\\x_1=\dfrac{-1-\sqrt{61}}{2}\ \ ,\ \ x_2=\dfrac{-1+\sqrt{61}}{2}\\\\\\2)\ \ x^2-45x-50=0\\\\D=2025+200=2225\\\\x_1=\dfrac{45-5\sqrt{89}}{2}\ \ ,\ \ \ x_2=\dfrac{45+5\sqrt{89}}{2}$

$3)\ \ 2x^2-2x-80=0\\\\D=644\\\\x_1=\dfrac{2-2\sqrt{161}}{4}=\dfrac{1-\sqrt{161}}{2}\ \ ,\ \ \ x_2=\dfrac{1-\sqrt{161}}{2}$

0 votes Thanks 1

NNNLLL54

Verified answer

$D=b^2-4ac$

$x_0=\dfrac{-b\underline+\sqrt{D}}{2a}$

$x^2+x-15=0\\D=1^2-4(-15)=61>0\ \ => \ \ 2 \ kopnya\\\\
x_1=\dfrac{-1-\sqrt{61}}{2}\\\\x_2=\dfrac{-1+\sqrt{61}}2$

$x^2-45x-50=0\\D=(-45)^2-4(-50)=2025+200=2225=25\cdot89=5^2\cdot89>0\ => \ 2 \ kopnya\\\\x_1=\dfrac{45-\sqrt{5^2\cdot89}}2=\dfrac{45-5\sqrt{89}}2\\\\x_2=\dfrac{45+\sqrt{5^2\cdot89}}2=\dfrac{45+5\sqrt{89}}{2}$

$2x^2-2x-80=0\\D=(-2)^2-4\cdot2(-80)=4+640=644=4^2\cdot161>0\ =>\ 2 \ kopnya\\\\x_1=\dfrac{2-\sqrt{4^2\cdot161}}{2\cdot2}=\dfrac{2-2\sqrt{161}}4=\dfrac{2(1-\sqrt{161})}{4}=\dfrac{1-\sqrt{161}}2\\\\x_2=\dfrac{2+2\sqrt{161}}{4}=\dfrac{2(1+\sqrt{161})}4=\dfrac{1+\sqrt{161}}2$

2 votes Thanks 0

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