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-+6x)=-3x д)(0,5x+1,,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)
$\displaystyle 4x^4-9=0\\\\(2x^2)^2-3^2=0\\\\(2x^2-3)(2x^2+3)=0\\\\2x^2=3; 2x^2=-3\\\\x^2=3/2; x^2 \neq -3/2\\\\ x=\pm \sqrt{1.5}$