Question

considere que x é R, resolva as equações:

a) (x-4)^2=81








b)(×+1)^2=100







c)(×+5)^2=-1


AJUDAAAAA!!!!!

Answer 1

a) (x-4)²=81
(x-4)(x-4)=81
x²-8x+16=81
x²-8x-65=0
a=1 b=-8 c=-65
∆=b²-4ac
∆=(-8)²-4.1.(-65)
∆=64+260
∆=324

x=-b±√∆ /2a
x1=-(-8)+√324 /2.1
x1=8+18 /2
x1=26/2
x1=13

x2=8-18 /2
x2=-10/2
x2=-5

S={-5;13}

b)(x+1)²=100
(x+1)(x+1)=100
x²+2x+1=100
x²+2x-99=0
a=1 b=2 c=-99

∆=2²-4.1.(-99)
∆=4+396
∆=400

x1=-2+√400 /2.1
x1=-2+20 /2
x1=18/2
x1=9

x2=-2-20 /2
x2=-22/2
x2=-11

S={-11;9}

c)(x+5)²=-1
(x+5)(x+5)=-1
x²+10x+25=-1
x²+10x+26=0
a=1 b=10 c=26

∆=10²-4.1.26
∆=100-104
∆=-4----->não existe, S=∅