Question

Решите уравнение: x^2-10x-12=0

Answer 1

Смотри решение.

Объяснение:

$x^2-10x-12=0\\a=1; b=-10; c=-12\\D=b^2-4ac\\D=(-10)^2-4*1*(-12)\\D=100-(-48)\\D=100+48\\D=148\\\sqrt{D}=\sqrt{148}=\sqrt{37*4}=\sqrt{37*2^2}=2\sqrt{37}\\x_{1}=\frac{-b+\sqrt{D}}{2a}=\frac{10+2\sqrt{37}}{2}=\frac{2(5+\sqrt{37})}{2}=5+\sqrt{37}\\x_{2}=\frac{-b-\sqrt{D}}{2a}=\frac{10-2\sqrt{37}}{2}=\frac{2(5-\sqrt{37})}{2}=5-\sqrt{37}\\$

Answer 2

$x^{2}-10x-12=0\\\\\frac{D}{4}=(-\frac{10}{2})^{2}+12=5^{2}+12=25+12=37\\\\x_{1}=5-\sqrt{37}\\\\x_{2}=5+\sqrt{37}$