Question

AJUTIR!! URGENT, va rog. Ex :
1, 2, 3 si 4

Answer 1

Răspuns:

$1) a) \sqrt{6} *(\frac{5\sqrt{3} }{\sqrt{6} } -\frac{2\sqrt{2} }{\sqrt{6} } )+2\sqrt{2} -3\sqrt{3} =\\=\sqrt{6} *\frac{5\sqrt{3}-2\sqrt{2} }{\sqrt{6} } +2\sqrt{2} -3\sqrt{3} =\\=5\sqrt{3}-3\sqrt{2}+2\sqrt{2}-3\sqrt{3}=2\sqrt{3} -\sqrt{2}$

$b)=2\sqrt{3}*( 6\sqrt{3} -5\sqrt{3} -3\sqrt{3}) =2\sqrt{3}*(-2\sqrt{3})=-4\sqrt{9} =-4*3=-12$

$c)=(\frac{4}{5\sqrt{2} }+\frac{3}{2\sqrt{2} } ) -(\frac{5}{2\sqrt{2} }- \frac{3\sqrt{2}*\sqrt{2} }{2\sqrt{2} } )=\\=(\frac{8}{10\sqrt{2} } +\frac{15}{10\sqrt{2} })-(\frac{5-3*2}{2\sqrt{2} })=\\ =\frac{23}{10\sqrt{2} }-(\frac{5-6}{2\sqrt{2} })=\frac{23}{10\sqrt{2} }+\frac{1}{2\sqrt{2} }=\\ =\frac{23}{10\sqrt{2} }+\frac{5}{10\sqrt{2} }=\frac{28}{10\sqrt{2} }=\frac{28\sqrt{2} }{20} =\frac{7\sqrt{2} }{5}$

2)a) 3(x+3) - 5(x+1)=4(x+4)

3x+9 -5x -5 =4x+16

3x-5x-4x =16-9+5

-6x=12

x= -2

b) |2x-3|=5

2x-3 =5

2x = 8

x =4

-(2x-3) =5

-2x+3=5

-2x =2

x = -1

$c) \frac{2(4x-3)}{6} -\frac{3(2x+1)}{6}= \frac{1*6+1}{6} \\\frac{8x-6}{6}-\frac{6x-3}{6}=\frac{7}{6} \\ 8x-6-6x-3=7\\ 2x-9=7\\2x=16\\x=8$

$d)|x-2|=\frac{1}{4}\\ x-2=\frac{1}{4} \\x=\frac{1}{4}+2\\ x=\frac{1}{4}+\frac{8}{4}\\ x=\frac{9}{4}\\ -(x-2) =\frac{1}{4} \\-x+2=\frac{1}{4}\\ -x=\frac{1}{4}-2\\ -x=\frac{1}{4}-\frac{8}{4}\\ -x=-\frac{7}{4}\\ x=\frac{7}{4}$

$e)x+3=\sqrt{25}\\ x+3=5\\x=2$

$3)a=2*12\sqrt{3} -3*5\sqrt{3} -7\sqrt{3} \\a=24\sqrt{3} -15\sqrt{3} -7\sqrt{3} \\a=2\sqrt{3} \\b=3*9\sqrt{3} -3*6\sqrt{3} -3\sqrt{3} \\b=27\sqrt{3} -18\sqrt{3} -3\sqrt{3} \\b=6\sqrt{3} \\mg=\sqrt{a*b} =\sqrt{2\sqrt{3}*6\sqrt{3} } =\sqrt{12*3} =\sqrt{36} =6$

$4)a)\left \{ {{2x-3y=17}|*(-3) \atop {3x+2y=6}|*2} \right. \\\left \{ {{-6x+9y=-51} \atop {6x+4y=12}} \right. \\/13y=-39\\y=-3\\2x-3*(-3)=17 \\2x+9=17\\2x=8\\x=4$

$b)\left \{ {{6x+3y-2x-4y+10=20} \atop {5x-5y+10=8x-4y+12-13}} \right. \\\left \{ {4x-y=10} \atop {5x-8x-5y+4y=-10+12-13}} \right. \\\left \{ {{4x-y=10} \atop {-3x-y=-11}|*(-1)} \right. \\\left \{ {{4x-y=10} \atop {3x+y=11}} \right. \\7x/=21\\x=3\\4*3-y=10\\12-y=10\\12-10=y\\y=2$

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