Question

5 Rezolvați ecuațiile, unde x este număr real:

d 2x²-16-16; e 3x²-5=25;

i 15x ^ 2 - 34 = - 4

c x²+8=8;

g - x ^ 2 + 24 = - 44 ; h 9+x²=27;

b -x²=25;

a x ^ 2 = - 4

f x ^ 2 + 7 = 15

6 Rezolvați ecuațiile, unde x este număr real:

a x ^ 2 = 29/16

e 1/3 * x ^ 2 = 64/27

d 2x ^ 2 = 72/25

i - 5x ^ 2 =-0,(5) .

; x ^ 2 = (4 * ∞)/81 ;

'h 12x ^ 2 =2,88;

b x ^ 2 = 169/196

g x ^ 2 =0,81;

f x ^ 2 / 4 = 75/12

Answer 1

5.

$\it a)\ \ \underbrace{x^2}_ {\geq0}=\ \underbrace{-4}_{ < 0} \Rightarrow S=\O\\ \\ \\ b)\ \ -x^2=25\Big|_{\cdot(-1)} \Rightarrow x^2=-25 \Rightarrow S=\O\\ \\ \\ d)\ 2x^2-16=16 \Big|_{+16} \Rightarrow 2x^2=32 \Big|_{:2} \Rightarrow x^2=16 \Rightarrow \sqrt{x^2}=\sqrt{16} \Rightarrow \\ \\ \\ \Rightarrow |x|=4 \Rightarrow x=\pm4 \Rightarrow S=\{-4,\ 4\}$

6.

$\it a)\ \ x^2=\dfrac{25}{16} \Rightarrow \sqrt{x^2}=\sqrt{\dfrac{25}{16}} \Rightarrow |x|=\dfrac{5}{4} \Rightarrow x=\pm\dfrac{5}{4}\\ \\ \\ b) \ \ x^2=\dfrac{169}{196} \Rightarrow \sqrt{x^2}=\sqrt{\dfrac{169}{196}} \Rightarrow |x|=\dfrac{13}{14} \Rightarrow x=\pm\dfrac{13}{14}$

$\it d)\ \ 2x^2=\dfrac{72}{25}\ \Big|_{\cdot\frac{1}{2}} \Rightarrow x^2=\dfrac{36}{25} \Rightarrow \sqrt{x^2}=\sqrt{\dfrac{36}{25}} \Rightarrow |x|=\dfrac{6}{5} \Rightarrow x=\pm\dfrac{6}{5}$