А))) 4*(2-3х)+7*(6х+1)-9*(9х+4)=30; _____8-12х+42х+7-81х-36=30; _____ 8+7-36-30=12х-42х+81х; ____ -51=51х; ____ Х=51:(-51); ____ Х=(-1). Проверка; 4*(2-3*(-1))+7*(6*(-1)+1)-9*(9*(-1)+4)= 4*(2+3)+7*(-6+1)-9*(-9+4)= 4*5+7*(-5)-9*(-5)= 20-35+45=30. ________________________________________________________________________________________________________________________________________
Б))) 17-2*(Х+3)+5*(Х-7)-3*(2х+1)=-28; ______
17-2х-6+5х-35-6х-3=-28; _____
17-6-35-3+28=2х-5х+6х; ____ 1=3х; ____ Х=1:3; ____ Х=1/3. Проверка; 17- 2*(1/3+3)+5*(1/3-7)-3*(2* 1/3+1)= 17- 2*(1/3+ 9/3)+ 5* (1/3- 21/3)- 3*(2/3+ 3/3)= 17- 2* 10/3+ 5* (-20/3)- 3* (5/3)= 17- 20/3 -100/3- 5= 12 -120/3= 12-40= -28. _______________________________________________________________________________________________________________________________________
В))) х*(4х+11)-7*(х^2-5х)=-3х*(Х+3); ___ 4х^2+ 11х- 7х^2- 35х= -3х^2- 9х; ___ -4х^2- 7х^2+ 3х^2+11х-35х+9х=0; ____ -8х^2-15х=0; D=(-15)^2 -4*(-8)*0= (-15)^2= 225. ____ D>0; _____ X1=(15-√225)/(2*(-8))= 0/(-16)=0; х2=(15+√225)/(2*(-8))= 30/(-16)= -1 14/16= -1 7/8. Проверка; X1=0; ___ 0*(4*0+11)-7*(0^2-5*0)=-3*0*(0+3); ___ 0=0; _________
x2=(-1 7/8); ___ (-1 7/8)= (- 15/8); ___ (-15/8)* (4* (-15/8)+11)- 7*( (-15/8)^2 -5* (-15/8)= -3* (-15/8)* ( (-15/8+ 3); ______
(-15/8)* (-60/8+ (11*8)/8 )- 7* (225/64+ (75*8)/64)= 45/8* (-15/8+ (3*8)/8 ); ________
(-15/8)* (-60/8+ 88/8)- 7* (225/64+ 600/64)= 45/8* (-15/8+ 24/8); _____ (-15/8)* (28/8)- 7* (825/64)= 45/8* (9/8); ______ (-420/64)- (5775/64)= 405/64; ___
-6195/64=405/64; Х2 не подходит; значит Х1=0; только;
________________________________________________________________________________________________________________________________________
А))) n*(12-n)-5=4n-n*(10+(n-3)); ____ 12n-n^2-5= 4n-10n-n^2+3n; ____ 12n-4n+10n-3n-n^2+n^2-5=0; ____ 15n-5=0; 15n=5; n=5:15; n=5/15= 1/3; ________ проверка 1/3*(12- 1/3)-5= 4* 1/3- 1/3* (10+ (1/3- 3)); ____ 1/3* (36/3- 1/3)- 5= 4/3- 1/3* (30/3+ (1/3- 9/3)); ____ 1/3* 35/3- 5= 4/3- 1/3* (30/3- 8/3); ______ 35/9- 45/9= 4/3- 1/3* 22/3; _______ (-10/9)= 4/3- 22/9; _____ (-1 1/9)= 12/9- 22/9; ______ (-1 1/9)= (-10/9); ______ (-1 1/9)= (-1 1/9). ________________________________________________________________________________________________________________________________________
Б))) 16+5*(-с-2*(с-4))=12*(3-2с)-1; _____ 16+5*(-с-2с+8)= 36-24с-1; ______
16+5*(-с-2с+8)=36-24с-1; ______
16-5с-10с+40=35-24с; _______
56-15с=35-24с; _________
(-15с)+24с=35-56; ______
9с=(-21); ______ с=(-21):9; с=(-21/9)=(-2 3/9)= (-2 1/3); _________
Проверка; (-2 1/3)= (-7/3); _____ 16+5*(-(-7/3)- 2*(-7/3)+8)=36-24*(-7/3)-1; _____
16+5* (7/3+14/3+ 24/3)= 36+ 56-1; ______ 16+5* (45/3)= 91; _____ 16+5* 15=91; ______ 16+75=91; ______ 91=91;