Question

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$x {}^{2} + 4x + 4 =19 + 8 \sqrt{3}$
va rog dau coroană, am nevoie ,va rog ​

Answer 1

Răspuns:x

Explicație pas cu pas:

x²+4x+4=19+8√3

(x+2)²=16+8√3+3

(x+2)²=4²+2*4*√3+√3²

(x+2)²=(4+√3)²

x+2=4+√3

x=4+√3-2

x=2+√3

Answer 2

$\it x^2+4x+4=x^2+2\cdot2\cdot x+2^2=(x+2)^2\\ \\ 19+8\sqrt3=16+3+8\sqrt3=4^2+2\cdot4\cdot \sqrt3+(\sqrt3)^2=(4+\sqrt3)^2$

Acum,   ecuația  devine:

$\it (x+2)^2+(4+\sqrt3)^2 \Rightarrow \sqrt{(x+2)^2}=\sqrt{(4+\sqrt3)^2} \Rightarrow |x+2|=4+\sqrt3 \Rightarrow \\ \\ \Rightarrow x+2=\pm(4+\sqrt2) \Rightarrow \begin{cases}\it x+2=-4-\sqrt3|_{-2} \Rightarrow x_1=-6-\sqrt3\\ \\ \it x+2=4+\sqrt3|_{-2} \Rightarrow x_2=2+\sqrt3\end{cases}$