Question

Решите уравнения:

а)2х+9=13-х         б)2.6-0.2b=4,1-0,5b  

 

в)3p-1-(p+3)=1    г)(13x-15)-(9+6x)=-3x   

 

д)(0,5x+1,2)-(3,6-4,5х)=(4,8-0,3х)+(10,5х+0,6)

 

е)6у+7 +8-5у =5   ж)х+1 - х-1 = 2 - х+3

     4        3               9       6            2

 

з)у³+3у²-у-3=0     и)4х⁴-9 =0

Answer 1

а)
$displaystyle 2x+9=13-x\\2x+x=13-9\\3x=4\\x=4/3$

б)
$displaystyle 2.6-0.2b=4.1-0.5b\\0.5b-0.2b=4.1-2.6\\0.3b=1.5\\b=1.5/0.3\\b=5$

в)
$displaystyle 3p-1-(p+3)=1\\3p-1-p-3=1\\2p=1+1+3\\2p=5\\ p=2.5$

г)
$displaystyle (13x-15)-(9+6x)=-3x \\ 13x-15-9-6x=-3x\\13x-6x+3x=15+9\\10x=24\\x=24/10\\x=2.4$

д)
$displaystyle (0,5x+1,2)-(3,6-4,5x)=(4,8-0,3x)+(10,5x+0,6)\\ 0.5x+1.2-3.6+4.5x=4.8-0.3x+10.5x+0.6\\0.5x+4.5x+0.3x-10.5x=4.8+0.6-1.2+3.6\\ -5.2x= 7.8\\x=-1.5$

е)
$displaystyle frac{6y+7}{4}+ frac{8-5y}{3}=5 | *12\\3(6y+7)+4(8-5y)=5*12\\18y+21+32-20y=60\\ -2y=7\\y= -3.5$

ж) 
$displaystyle frac{x+1}{9}- frac{x-1}{6}=2- frac{x+3}{2}| *18\\ 2(x+1)-3(x-1)=2*18-9(x+3)\\2x+2-3x+3=36-9x-27\\2x-3x+9x=36-27-2-3\\ 8x= 4\\x= 0.5$

з)
$displaystyle y^3+3y^2-y-3=0\\y^2(y+3)-(y+3)=0\\(y+3)(y^2-1)=0\\y=-3; y^2=1\\y=-3; y=1; y=-1$

и)
$displaystyle 4x^4-9=0\\(2x^2)^2-3^2=0\\(2x^2-3)(2x^2+3)=0\\2x^2=3; 2x^2=-3\\x^2=3/2; x^2 neq -3/2\\ x=pm sqrt{1.5}$