Question

5. Решите уравнение: |4x^2 + 4х | –1 = 0. срочно!!!!

Answer 1

Ответ:

Объяснение:

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Answer 2

$\displaystyle\bigg|4x^2+4x\bigg|-1=0\Leftrightarrow\bigg|4x^2+4x\bigg|=1.\\1)~4x^2+4x=1\Leftrightarrow 4x^2+4x-1=0. \\D=4^2-4\cdot4\cdot(-1)=16+16=32=\bigg(4\sqrt{2} \bigg)^2.\\x_1=\frac{-4-4\sqrt{2} }{8} =\frac{4\bigg(-1-\sqrt{2}\bigg) }{8} =\frac{-1-\sqrt{2} }{2} .\\x_2=\frac{-4+4\sqrt{2} }{8} =\frac{-1+\sqrt{2} }{2} .\\2)~4x^2+4x=-1\Leftrightarrow \underbrace{4x^2+4x+1}_{a^2+2ab+b^2=(a+b)^2} =0\Rightarrow (2x+1)^2=0.\\2x+1=0\Rightarrow 2x=-1\Rightarrow x=-1:2=-0,5.\\\bf OTVET:$

$\bf x_1=\dfrac{-1-\sqrt{2} }{2} ~;~x_2=-0,5~;~x_3=\dfrac{-1+\sqrt{2} }{2} .$