Question

a) (x-1)²=x+5=

b) (3x-2)²+(2-x)²=

c) x²-2x=1 + x
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4 4 2

Answer 1

Oiii

A)
(x-1)²=x+5
x²  -2x +1 = x+5
x² - 2x +1 -x -5 =0
x² -3x -4 =0

por baskara

a=1, b=-3, c=-4

Δ=b²-4ac
Δ=(-3)²-4.1.(-4)
Δ=9+16
Δ=25

x = -b ± √Δ /2a
x = -(-3) ± √25 /2.1
x = 3 ± 5 /2

x¹ = 3+5=8/2= 4
x² = 3-5= -2/2 = -1

S={4, -1}

b)
(3x-2)²+(2-x)²
9x² - 12x +4 + 4 - 4x + x²
10x² - 16x +8

Por baskara

a=10, b=-16, c=8

Δ=b²-4ac
Δ=(-16)²-4.10.8
Δ=256-320
Δ= - 64

paramos por aqui

c)
x²-2x=1 + x
x²-2x-1-x=0
x²-3x-1=0

por baskara

a=1, b=-3, c=-1

Δ=b²-4ac
Δ=(-3)²-4.1.(-1)
Δ=9+4
Δ=13

x = -b ± √Δ /2a
x = -(-3) ± √13 /2.1
x = 3 ± √13 /2

$x^1 = \frac{3+ \sqrt{13} }{2}$

$x^2 = \frac{3- \sqrt{13} }{2}$

$S=[ { \frac{3+ \sqrt{13} }{2}, \frac{3- \sqrt{13} }{2}]$