Question

Va rog sa ma ajutati si pe mine

Answer 1

$1).-5a+7a-11a+16a=2a-11a+16a=-9a+16a=7a \\ 2).(4x+5y)-(6x-7y)-(-5x+6y)= \\ =4x+5y-6x+7y-5x-6y= -7x+6y \\ 3).(-6 \sqrt{3} +5 \sqrt{2} )x-(7 \sqrt{2} -4 \sqrt{3} )x= \\ =-6 \sqrt{3} x+5 \sqrt{2} x-7 \sqrt{2} x+4 \sqrt{3} x=-2 \sqrt{3} x-2 \sqrt{2} x$
$4).(4 \sqrt{3} - \sqrt{27} )a+( \sqrt{75} - \sqrt{108} )a-(2 \sqrt{48} -3 \sqrt{112} )a= \\ =(4 \sqrt{3} -3 \sqrt{3} )a+(5 \sqrt{3} -6 \sqrt{3} )a-(2*4 \sqrt{3} -3*4 \sqrt{7} )a= \\ = \sqrt{3} a- \sqrt{3} a-(8 \sqrt{3} -12 \sqrt{7} )a= \sqrt{3} a- \sqrt{3} a-8 \sqrt{3} a+12 \sqrt{7} a= \\ =-8 \sqrt{3} a+12 \sqrt{7} a$
$5).a \sqrt{( \sqrt{3}-3)^2 } -a \sqrt{(2+ \sqrt{3} )^2} -a \sqrt{(2 \sqrt{3} -4)^2} = \\ =a| \sqrt{3} -3|-a|2+ \sqrt{3} |-a|2 \sqrt{3} -4|= \\ =a(3- \sqrt{3} )-a(2+ \sqrt{3} )-a(4-2 \sqrt{3} )= \\ =3a- \sqrt{3} a-2a- \sqrt{3} a-4a+2 \sqrt{3} a=-3a$
$6).(2x+3)(x-2)-2(x^2-x-3)= \\ =2x^2-4x+3x-6-2x^2+2x+6=x$
$1).3 \sqrt{18} x-7 \sqrt{32} x+4 \sqrt{72} x-2 \sqrt{50} x+3 \sqrt{8} x= \\ =3*3 \sqrt{2}x -7*4 \sqrt{2} x+4*6 \sqrt{2} x-2*5 \sqrt{2} x+3*2 \sqrt{2} x= \\ =9 \sqrt{2} x-28 \sqrt{2} x+24 \sqrt{2} x-10 \sqrt{2} x+6 \sqrt{2} x=x \sqrt{2}$
$2).2 \sqrt{(1- \sqrt{3} )^2} x+ \sqrt{( \sqrt{3} -2)^2} x+x \sqrt{(2 \sqrt{3} -4)^2} - \sqrt{( \sqrt{3} -4)^2} x= \\ =2|1- \sqrt{3} |x+| \sqrt{3} -2|x+x|2 \sqrt{3} -4|-| \sqrt{3} -4|x= \\ =2( \sqrt{3} -1)x+(2- \sqrt{3} )x+x(4-2 \sqrt{3} )-(4- \sqrt{3} )x= \\ =2 \sqrt{3} x-2x+2x- \sqrt{3} x+4x-2 \sqrt{3} x-4x+ \sqrt{3} x= 0$
$3). \sqrt{(1- \sqrt{2} )^2} a+ \sqrt{(4-3 \sqrt{2} )^2} a- \sqrt{(7-5 \sqrt{2} )^2} a- \sqrt{( \sqrt{2} -3)^2} a= \\ =|1- \sqrt{2} |a+|4-3 \sqrt{2} |a-|7-5 \sqrt{2} |a-| \sqrt{2} -3|a= \\ =( \sqrt{2} -2)a+(3 \sqrt{2} -4)a-(5 \sqrt{2} -7)a-(3- \sqrt{2} )a= \\ = \sqrt{2} a-2a+3 \sqrt{2} a-4a-5 \sqrt{2} a+7a-3a+ \sqrt{2} a=-2a$
$1).a=3(4 \sqrt{2} -3 \sqrt{3} )x+( \frac{6}{ \sqrt{3} } + \frac{18}{ \sqrt{2} })* \sqrt{6} x-x( \frac{4}{ \sqrt{2} } + \frac{9}{ \sqrt{3} } )* \sqrt{24} \\ a=12 \sqrt{2} x -9 \sqrt{3} x+( \frac{6 \sqrt{3} }{3} + \frac{18 \sqrt{2} }{2} )* \sqrt{6} x-x( \frac{4 \sqrt{2} }{2} + \frac{9 \sqrt{3} }{3} )*2 \sqrt{6} \\ a=12 \sqrt{2} x-9 \sqrt{3} x+(2 \sqrt{3} +9 \sqrt{2} )* \sqrt{6} x-x(2 \sqrt{2} +3 \sqrt{3} )*2 \sqrt{6}$
$a=12 \sqrt{2} x-9 \sqrt{3} x+2 \sqrt{18} x+9 \sqrt{12} x-4 \sqrt{12} x-6 \sqrt{18} x \\ a=12 \sqrt{2} x-9 \sqrt{3} x+2*3 \sqrt{2} x+9*2 \sqrt{3} x-4*2 \sqrt{3} x-6*3 \sqrt{2} x \\ a=12 \sqrt{2} x-9 \sqrt{3} x+6 \sqrt{2} x+18 \sqrt{3} x-8 \sqrt{3} x-18 \sqrt{2} x \\ a= \sqrt{3} x$