Question

помогите с уравнениями

Answer 1

$1) x^{2} =9\x=+-3 \ \ 2)( x^{2} -2x+1) ^{2} =1^{2} \ ( x^{2} -2x+1) ^{2} -1^{2} =0\( x^{2} -2x+1-1=0)( x^{2} -2x+1+1)=0 \ x^{2} -2x=0\x(x-2)=0\x=0\x-2=0\x=0$

$x^{2} -2x+2=0\D=4+8=12 \ sqrt{D} = sqrt{3*4} =2 sqrt{3} \ x_{1} = frac{2+2 sqrt{3} }{2} = frac{2(1+ sqrt{3} )}{2} =1+ sqrt{3} \ \ x_{1} = frac{2-2 sqrt{3} }{2} = frac{2(1- sqrt{3} )}{2} =1- sqrt{3}$

$3)(x+1)^{2} =(2x+5)^{2} \ x^{2} +1+2x=4 x^{2} +25+20x \ x^{2} +1+2x-4 x^{2} -25-20x=0\-3 x^{2} -18x-24=0/*(-1)\3 x^{2} +18x+24=0/:3\ x^{2} +6x+8=0\D=36-32=4 \ sqrt{D} =2 \ x_{1} = frac{-6-2}{2} = frac{-8}{2} =-4 \ \ x_{2} = frac{-6+2}{2} = frac{-4}{2} =-2$

$4)2 x^{2} -7x+5=0\D=49-40=9 \ sqrt{D} =3 \ x_{1} = frac{7+3}{4} = frac{10}{4} =2.5 \ x_{2} = frac{7-3}{4} = frac{4}{4} =1$

$5)3 x^{2} -7x+5=0\D=49-60<0$


$6) x^{2} -2011x+2010=0 \ D=2011^{2} -4*2010=2009^{2} \ sqrt{D} =2009 \ x_{1} = frac{2011-2009}{2} = frac{2}{2} =1 \ x_{2} = frac{2011+2009}{2} = frac{4020}{2} =2010$

$7) x^{2} -2010x-2011=0\D=(-2010 )^{2} +4*2011=2012^{2} \ sqrt{D} =2012 \ x_{1} = frac{2010-2012}{2} =-1 \ x_{2} = frac{2010+2012}{2} =2011$

$8)2 x^{4} -7 x^{2} +5=0\ x^{2} =t\2t ^{2} -7t+5=0\D=49-40=9 \ sqrt{D} =3\t_{1} = frac{7+3}{4} = frac{10}{4} =2.5 \ t _{2} = frac{7-3}{4} =1 \ x^{2} =2.5\x=+- sqrt{2.5} \ x^{2} =1\x=+-1$