4=(4(2+3)) / 4=2+3Exercicios P.811. Resolva as equacoes, nao esquecendo de fazer averificacao dos valores encontrados.a) (3x)=6(3x)2=623x=36X=36/3X=12b) (3x-2)=5(3x-2)2=523x-2=253x=25+23x=27X=9c) (2x+1)=-3(2x+1)2=(-3)22x+1=92x=8X=8/2X=4 a Nao deu certod) 2x=4(2x)2=4222x2=164x=16X=16/4X=4e) 3x=12(3x)2=12232x2=1449x=144X=144/9X=16f) (x2+3x-9)=x(x2+3x-9)2=x2x2+3x-9=x2x2-x2+3x=93x=9X=9/3X=3g) (2x+5)=(x+8)(2x+5)2= (x+8)22x+5= x+82x-x=8-5X=3h) 32x=6(32x)2=623222x2=369*2x=3618x=36X=22. Determine o conjunto solucao da equacao(x2+2)=x+1.(x2+2)=x+1(x2+2)2=(x+1)2x2+2=x2+2x+1x2-x2-2x=1-2-2x=-1 -x=-1/2 (-1)X=1/23. Qual e o valor real de x na equacao?(5x+2)=(-6+9x)(5x+2)2=(-6+9x)25x+2=-6+9x5x-9x=-6-2-4x=-8-X=-8/4-x=-2 (-1)X=24. Determine o numero x para que se tenha(x-5)=3/(x-5), com x=5.(x-5)2=(3/(x-5))2x-5=32/(x-5)2x-5=9/(x-5)(x-5)2=9x2-10x+25=9x2-10x+16=0=b2-4ac=102-4(1)(16)=100-64=36X=(-b)/2aX=(-(-10) 36)/2(1)X=(106)/2X=(10+6)/2X=16/2X=8X=(10-6)/2X=4/2X=2S={8 e 2}Exercicios P.851. Racionalize o denominador das seguintesexpressoes:a) 2 / 10=210 / 102=2 10/ 10=10/ 5b) 6 / 6=66 / 62=66 / 6=6c) 9 / 3=93 / 32=93 / 3=33d) 5 / 2= (5 * 2) / 22=10 / 2e) 20 / (25)=205 / (252)=205 / (2*5)=205 / 10=25f) 3 / 6=36 / 62=36 / 6=6 / 2g) 20 / (310)= (2010) / (3102)= (2010) / (3*10)= (2010) / 30= (210) / 3h) 1 / 7=7 / 72=7 / 7i) (23) / (52)= (23) / (52)= (23*2) / (522)= (26) / (5*2)= (26) / 10=6 / 5j) (73)/ (27)= (73*7) / (272)= (721) / (2*7)= (721) / 14=21 / 22. Racionalize o denominador das expressoesseguintes:a) (1-3)/ 3= (1-3) 3 / 32= (3-32) / 3= (3-3) / 3b) (3-2)/ 2= (3-2) 2/ 22= (32-22) / 2 = (32-2) / 2c) (5+2)/ 5= (5+2) 5 / 52= (52+2*5) / 5= (5+10) / 53. Sabendo que x e y sao numeros reais positivos,racionalize o denominador das seguintes expressoes:a) x /x=xx /x2=x x /x=x b) x/(2y)=xy /(2y2)=xy /(2y)c) (xy) /(5x)=(xyx) / (5x2)=yx / 5d) (xy)/ (yx)= (xy*x) / (yx2)= (x(xy)) / (yx)= (xy) / y4. Voce sabe que n(a/b)= na/ nb. Racionalize o denominador das expressoes:a) (3/10)=3/10= (3*10)/102=30/10b) (5/3)=5/3= (5*3)/32=15/3c) (1/2)=1/2=2/22=2/2d) (1/8)=(1/8)=(23/82)=2(2/8)=2/4e) 0,9=(9/10)=9/10= (9*10) / 102=90/10=(2*32*5)/10=310/10f) (5/8)=5/8= (5*8) / 82=40/8=(23*5)/8=2(2*5)/8=10/45. Considerando 6=2,449, 2=1,414 e 10=3,162,calcule o valor na forma decimal das expressoes:a) (3/2)=3/2= (3*2)/ 22=6/2=2,449/2=1,2245b) (2/5)=2/5= (2*5)/ 52=10/5=3,162/5=0,6324c) (1/2)=1/2=2/22=2/2=1,414/2=0,7076. Racionalize o denominador das expressoes asegui:a) 1 / 563=562 / 563=562 / 563 * 562=562/ 565=562/6b) 15 / 35=15 352 / 35 *352=15 352 / 353=15 352 / 5=3 352 c) 2 / 927=2 922/ 927*922=2 922/ 929=2 922/ 2=922d) 6 / 1035=6 1035/ 1035* 1035=6 1035/ 10310=6 1035/ 3=21035e) 4/483=448/483 *48=448/484=4484/8=48/2f) 20 11103/11108 *11103=20 11103/ 111011=20 11103/ 10=2 111037. Racionalize o denominador das seguintesexpressoes:a) 1/(3-6)=1(3+6)/(3-6) (3+6)= (3+6) / (32-62)= (3+6) / (9-6)= (3+6) / 3b) 2/(5+3)=2(5-3) / (5+3) (5-3)= (25-23)/(5-3)= (25-23)/2=5-3c) 1/(4-5)=1(4+5)/(4-5)(4+5)= (4+5) / (42-52)= (4+5)/(16-5)= (4+5)/ 11d) 11/(23-1)= (223+11) / (432-12)= (223+11) / (4*3-1)= (11+223) / (12-1)= (11(1-23)) / 11=1+23e) (2-2)/ (3+2)= ((2-2)(3-2)) / ((3+2)(3-2))= (2*3-22-32+22) / (32-22)= (6-52+2) / (9-2)= (8-52) /7f) (2-22)/ (2-2)= ((2-22)(2+2)) / ((2-2)(2+2))= (4+22-42-222) / (22-22)= (4-22-2*2) / (4-2)= (4-22-4) / 2= (-22)/2=-2g) (1+5) / (3+5)= (1+5)( 3-5) / ((3+5)(3-5))= (3-5+15-52) / (32-52)= (3-5+15-5) / (3-5)= (3-5+15-5) / -2= (-3+5-15+5) / 2h) (3-2)/ (3+2)= (3-2)(3-2) / (3+2)(3-2)= (32-26+22) / (3-2)= (3-26+2) / 1=5-26