Question

ex 7 si 8 pls urgent dau coroana​

Answer 1

$\displaystyle 7.\\ a)\frac{1}{36} x^2=0,25 \Rightarrow x^2=0,25 \cdot 36 \Rightarrow x^2=9 \Rightarrow x=\pm\sqrt{9} \Rightarrow \boxed{x_1=-3}\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\Rightarrow \boxed{x_2=3}$

$\displaystyle b)~\frac{1}{6,4}x^2=2,5 \Rightarrow x^2=2,5 \cdot 6,4 \Rightarrow x^2= 16 \Rightarrow x=\pm\sqrt{16} \Rightarrow \boxed{x_1=-4}\\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\Rightarrow \boxed{x_2=4}$

$\displaystyle c)~\frac{1}{16} x^2=2,25 \Rightarrow x^2=2,25 \cdot 16 \Rightarrow x^2=36 \Rightarrow x=\pm\sqrt{36} \Rightarrow \boxed{x_1=-6}\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\Rightarrow \boxed{x_2=6}$

$\displaystyle d)~\frac{1}{25}x^2=2,56 \Rightarrow x^2=2,56 \cdot 25 \Rightarrow x^2= 64 \Rightarrow x=\pm \sqrt{64}\Rightarrow \boxed{x_1=-8}\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\Rightarrow \boxed{x_2=-8}$

$\displaystyle e)~\frac{1}{64}x^2=0,25 \Rightarrow x^2=0,25 \cdot 64 \Rightarrow x^2= 16 \Rightarrow x=\pm\sqrt{16}\Rightarrow \boxed{x_1=-4} \\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\Rightarrow \boxed{x_2=4}$

$\displaystyle f)~\frac{1}{225} x^2=1,44\Rightarrow x^2=1,44 \cdot 225 \Rightarrow x^2=324 \Rightarrow x=\pm \sqrt{324} \Rightarrow \boxed{x_1=-18}\\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\Rightarrow \boxed{x_2=18}$

$\displaystyle g)~\frac{1}{36}x^2=2,25 \Rightarrow x^2=2,25 \cdot 36 \Rightarrow x^2= 81 \Rightarrow x=\pm \sqrt{81} \Rightarrow \boxed{x_1=-9}\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\Rightarrow \boxed{x_2=9}$

$\displaystyle h)~\frac{1}{10} x^2=6,4 \Rightarrow x^2=6,4 \cdot 10 \Rightarrow x^2=64 \Rightarrow x=\pm\sqrt{64}\Rightarrow \boxed{x_1=-8}\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\Rightarrow\boxed{x_2=8}$

$\displaystyle 8.\\ a)~x^2=9\Rightarrow x=\pm \sqrt{9} \Rightarrow \boxed{x_1=-3}\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\Rightarrow\boxed{x_2=3}\\\\x\in\{-3;3\}\\\\ b)~3x^2=12 \Rightarrow x^2=\frac{12}{3} \Rightarrow x^2=4 \Rightarrow x=\pm \sqrt{4} \Rightarrow \boxed{x=-2}\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\Rightarrow \boxed{x=2}\\\\ x\in \{-2;2\}$

$\displaystyle c)~2x^2-72=0 \Rightarrow 2x^2=0+72 \Rightarrow 2x^2=72 \Rightarrow x^2=\frac{72}{2} \Rightarrow x^2=36 \Rightarrow \\\\ \Rightarrow x=\pm \sqrt{36} \Rightarrow \boxed{x_1=-6}\\\\~~~~~~~~~~~~~~~~~~\Rightarrow \boxed{x_2=6}\\\ x\in\{-6;6\}$

$\displaystyle d)~(x-2)^2=25 \Rightarrow x^2-2 \cdot x \cdot 2+2^2=25 \Rightarrow x^2-4x+4=25 \Rightarrow \\\\ \Rightarrow x^2-4x+4-25 =0\Rightarrow x^2-4x-21=0\\\\ \Delta=(-4)^2-4 \cdot 1 \cdot (-21)=16 +84=100 > 0\\\\ x_1=\frac{-(-4)-\sqrt{100} }{2 \cdot 1}\Rightarrow x_1=\frac{4-10}{2} \Rightarrow x_1=\frac{-6}{2} \Rightarrow \boxed{x_1=-3}\\\\ x_2=\frac{-(-4)+\sqrt{100} }{2 \cdot 1}\Rightarrow x_2=\frac{4+10}{2} \Rightarrow x_2=\frac{14}{2} \Rightarrow \boxed{x_2=7}\\\\ x\in\{-3;7\}$

$\displaystyle e)~(2x-3)^2=25 \Rightarrow (2x)^2-2 \cdot 2x \cdot 3+3^2=25 \Rightarrow 4x^2-12x+9-25 =0\Rightarrow \\\\ \Rightarrow 4x^2-12x-16=0\\\\ \Delta=(-12)^2-4 \cdot 4 \cdot (-16)=144+256=400 > 0\\\\ x_1=\frac{-(-12)-\sqrt{400} }{2 \cdot 4} \Rightarrow x_1=\frac{12-20}{8} \Rightarrow x_1=\frac{-8}{8} \Rightarrow \boxed{x_1=-1}\\\\ x_2=\frac{-(-12)+\sqrt{400} }{2 \cdot 4}\Rightarrow x_2=\frac{12+20}{8} \Rightarrow x_2=\frac{32}{8} \Rightarrow \boxed{x_2=4} \\\\ x\in\{-1;4\}$

$\displaystyle f)~(2x+1)^2=49\Rightarrow (2x)^2+2 \cdot 2x \cdot 1+1^1=49\Rightarrow 4x^2+4x+1-49 =0\Rightarrow \\\\ \Rightarrow 4x^2+4x-48=0\\\\ \Delta=4^2-4 \cdot 4 \cdot (-48)=16+768=784 > 0\\\\ x_1=\frac{-4-\sqrt{784} }{2 \cdot 4} \Rightarrow x_1=\frac{-4-28}{8} \Rightarrow x_1=\frac{-32}{8} \Rightarrow \boxed{x_1=-4}\\\\ x_2=\frac{-4+\sqrt{784} }{2 \cdot 4}\Rightarrow x_2=\frac{-4+28}{8} \Rightarrow x_2=\frac{24}{8} \Rightarrow \boxed{x_2=3} \\\\ x\in \{-4;3\}$