Question

109)Resolva as equações abaixo e encontre o valor de x

a)x2 - 81=0
b)2x2 - 242=0
c)2x2 - 6x=0
d)5x2 - 15x =0
e)9x2 +24x + 16=0
f)x2 - 12x + 36=0
g)x2 + 14x + 49=0
022h)x2 - 16x + 64=0​

Answer 1

Resposta:

símbolos $±$=±       $Δ$=Δ

Explicação passo-a-passo:

A)

$x^{2}-81=0\\x^{2}=81\\x=\sqrt{81} \\± 9$

B)

$2x^{2}-242=0\\2x^{2}=242\\x^{2}=242/2\\x=\sqrt{121} \\x=±   11$

C)

$2x^{2}-6=0\\Δ=-6x^{2}-4*2*0\\Δ=36-0\\ Δ=36$

$x=6± \sqrt[2]{36} /2*2\\x=6±6/4\\x'=6+6/4=12/4=3\\ x''=6-6/4=0/4=0$

D)

$5x^{2}-15x=0\\Δ=-15^{2} -4*5*0\\Δ=225-0\\Δ=225\\x=15±\sqrt{225}/2*5\\x=15±15/10\\x'=15+15/10= 30/10= 3\\x''=15-15/10= 0/10= 0$

E)

$9x^{2}+24x+16\\Δ=24^{2}-4*9*16\\Δ=576+576\\Δ=0\\x=-24± \sqrt{0}/2*9\\x'=-25+0/18=-25/18$

F)

$x^{2} -12x+36=0\\\\Δ=-12^{2}-4*1*36\\Δ=144-144\\Δ=0\\x=12± \sqrt{0}/2\\x=12+0/2=12/2=6$

G)

$x^{2}+14*+49=0\\Δ=14^{2}-4*1*49\\Δ=196-196\\Δ=0\\x=14± \sqrt{0} /2\\\\x=14+0/2=14/2=7$

H)

$x^{2}-16+64=0\\Δ-16^{2}-4*1*64\\Δ=256-256\\Δ=0\\x=16± 0\\x=16+0/2=16/2=8$