Question

Exercitiile incercuite!

Answer 1

2)  (x-2)²-(x²+1)= -1 => x²-4x+4 -x²-1=-1
4=4x=> x=1

3)     A1= 95*4+=380+76x
A2=(80-4)*(95-x)=7220-76x
=> 380+76x=7220-76x
=> 152x=6840
x=45 m

4)  
Notam cu M : DM_|_EC
CB=EA=DM=x
EC=AB=30
 Aria ABCDE=450
AB*CB+DM*EC:2=450
30x+30x:2=30x+15x=45x =450 => x=10

5)$2*( \frac{x-2}{3})+ \frac{1}{2} ( \frac{x-2}{3})=\frac{x-2}{3}+0,75$
$2*( \frac{x-2}{3})+ \frac{1}{2} ( \frac{x-2}{3})-\frac{x-2}{3}= \frac{3}{4}$
$( \frac{x-2}{3})(2+ \frac{1}{2}-1)= \frac{3}{4}$
$\frac{x-2}{3}* \frac{3}{2}=\frac{x-2}{2}= \frac{3}{4} =\ \textgreater \ x-2= \frac{3}{2}$
$x= \frac{3}{2}+2=\ \textgreater \ x= \frac{7}{2} =3,5$

$0.5( \frac{2x- \sqrt{2} }{ \sqrt{3}} )- \frac{2}{3} ( \frac{ \sqrt{2}-2x }{ \sqrt{3}} )=( \frac{ \sqrt{3} }{ \sqrt{2}( \sqrt{2}x-1) })^{-1 } + \frac{1}{5}$
$\frac{1}{2}( \frac{2x- \sqrt{2} }{ \sqrt{3}} )+ \frac{2}{3} ( \frac{ 2x- \sqrt{2} }{ \sqrt{3}} )=( \frac{ \sqrt{3} }{2x- \sqrt{2} })^{-1 } + \frac{1}{5}$
$\frac{1}{2}( \frac{2x- \sqrt{2} }{ \sqrt{3}} )+ \frac{2}{3} ( \frac{ 2x- \sqrt{2} }{ \sqrt{3}} )- \frac{2x- \sqrt{2} }{ \sqrt{3}}= \frac{1}{5}$
$( \frac{2x- \sqrt{2} }{ \sqrt{3}} )*( \frac{1}{2} + \frac{2}{3} - 1 )= \frac{1}{5}$
$( \frac{2x- \sqrt{2} }{ \sqrt{3}} )* \frac{1}{6} = \frac{1}{5} =\ \textgreater \ \frac{2x- \sqrt{2} }{ \sqrt{3}} = \frac{6}{5}$
$2x- \sqrt{2} = \frac{6\sqrt{3}}{5} =\ \textgreater \ 2x= \frac{6\sqrt{3}}{5} + \sqrt{2} =\frac{6\sqrt{3}+5\sqrt{2}}{5}$
$x=\frac{6\sqrt{3}+5\sqrt{2}}{10}$