Đáp án:
$\displaystyle \begin{array}{{>{\displaystyle}l}} Bài\ 9:\\ a.1000\ ;\ b.\ -2100;\ c.\ 7000;\ d.\ 7600;\ e.\ 3\ ;\ f.5320\\ Bài\ 10:\\ a.\ x=4\ hoặc\ x=3;\ b.\ x=\frac{-1}{4} ;\ c.\ x=0\\ d.\ x=\frac{2}{3} ;\ e.\ x=5;\ f.\ x=\frac{1}{2} \end{array}$
Giải thích các bước giải:
$\displaystyle \begin{array}{{>{\displaystyle}l}} Bài\ 9:\\ a.\ 35^{2} -15^{2} =( 35-15)( 35+15) =20.50=1000\\ b.\ 48^{2} -42^{2} +64-52^{2}\\ =\left( 48^{2} -52^{2}\right) -\left( 42^{2} -8^{2}\right)\\ =( 48-52)( 48+52) -( 42-8)( 42+8)\\ =-4.100-50.34=100.( -4-17) =-2100\\ c.\ 85^{2} -15^{2} =( 85-15)( 85+15) =70.100=7000\\ d.\ 72^{2} +144.16+16^{2} -12^{2} =72^{2} +2.72.16+16^{2} -12^{2}\\ =( 72+16)^{2} -12^{2} =88^{2} -12^{2} =( 88+12)( 88-12) =76.100=7600\\ e.\ \frac{43^{2} -11^{2}}{( 36,5)^{2} -( 27,5)^{2}} =\frac{( 43-11)( 43+11)}{( 36,5-27,5)( 36,5+27,5)}\\ =\frac{32.54}{9.64} =\frac{2^{5} .3^{3} .2}{3^{2} .2^{6}} =3\\ f.\ 73^{2} -13^{2} -10^{2} +20.13=( 73-13)( 73+13) -10.( 10-26)\\ =60.86+10.16=10.( 6.86+16) =10.532=5320\\ Bài\ 10:\\ a.\ x-3=( 3-x)^{2}\\ \Leftrightarrow x-3-9+6x-x^{2} =0\\ \Leftrightarrow -x^{2} +7x-12=0\\ \Leftrightarrow -x^{2} +3x+4x-12=0\\ \Leftrightarrow -x( x-3) +4( x-3) =0\\ \Leftrightarrow ( -x+4)( x-3) =0\\ \Leftrightarrow -x+4=0\ hoặc\ x-3=0\\ \Leftrightarrow x=4\ hoặc\ x=3\\ b.\ x^{3} +\frac{3}{2} x^{2} +\frac{3}{4} x+\frac{1}{8} =\frac{1}{64}\\ \Leftrightarrow x^{3} +\frac{1}{4} x^{2} +\frac{5}{4} x^{2} +\frac{5}{16} x+\frac{7}{16} x+\frac{7}{64} =0\\ \Leftrightarrow x^{2}\left( x+\frac{1}{4}\right) +\frac{5}{4} x\left( x+\frac{1}{4}\right) +\frac{7}{16}\left( x+\frac{1}{4}\right) =0\\ \Leftrightarrow \left( x^{2} +\frac{5}{4} x+\frac{7}{16}\right)\left( x+\frac{1}{4}\right) =0\\ \Leftrightarrow x=\frac{-1}{4}\\ c.\ ( 2x-5)^{2} -( 5+2x)^{2} =0\\ \Leftrightarrow 4x^{2} -20x+25-\left( 25+20x+4x^{2}\right) =0\\ \Leftrightarrow -40x=0\Leftrightarrow x=0\\ d.Sửa\ đề:\ 27x^{3} -54x^{2} +36x=8\\ \Leftrightarrow 27x^{3} -54x^{2} +36x-8=0\\ \Leftrightarrow ( 3x-2)^{2} =0\Leftrightarrow 3x-2=0\Leftrightarrow x=\frac{2}{3}\\ e.\ x^{2} -10x=-25\\ \Leftrightarrow x^{2} -10x+25=0\\ \Leftrightarrow ( x-5)^{2} =0\Leftrightarrow x-5=0\Leftrightarrow x=5\\ f.\ 4x^{2} -4x=-1\\ \Leftrightarrow 4x^{2} -4x+1=0\Leftrightarrow ( 2x-1)^{2} =0\Leftrightarrow 2x-1=0\Leftrightarrow x=\frac{1}{2} \end{array}$
