Question

equação irracional resolva : raiz quadrada de x - 1 = x - 3

Answer 1

√x-1=x-3

(√x-1)^2=(x-3)^2

x^2-6x+9=x-1

x^2-6x-x+9+1=0

x^2-7x+10=0

∆=b^2-4.a.c

∆=(-7)^2-4.1.(10)

∆=49-40

∆=9

x1=7+3/2

x1=10/2

x1=5

x2=7-3/2

x2=5/2

s={5/2,5}

Answer 2

Olá!
$Domínio : x - 1 > 0 \\ x > 1$

$\sqrt{x - 1} = x - 3 \\ → ({\sqrt{x - 1}})^{2} = {(x - 3)}^{2} \\ →x - 1 = {x}^{2} - 2.3x + {3}^{2} \\ →x - 1 = {x}^{2} - 6x + 9 \\ → {x}^{2} - 6x - x+ 9 + 1 = 0 \\ → {x}^{2} + - 7x + 10 = 0$
a = 1
b = –7
c = 10
∆ = b² –4ac
∆ = (–7)² –4.1.10
∆ = 49 –40
∆ = 9
$x = \frac{ - ( - 7) ± \sqrt{9} }{2.1} \\ x = \frac{ 7 ± 3}{2} \\ x'= \frac{ 7 + 3}{2} = \frac{10}{2} = 5 \\ x'' = \frac{ 7 - 3}{2} = \frac{4}{2} = 2$
S = { 2,5}

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