Question

01 - Resolva as equações em R.

a) (3x + 1)² = 0

b) (2x - 4)² = 0

c) (x - 3)²= - 2x²

d) x(x - 5) = -6

e) x(3x + 4) = -1

Answer 1

a)(3×+1)²=0

(3×+1)(3×+1)=0

9ײ+3×+3×+2=0

9ײ+6×+2=0

∆=36-72

∆=-36

S={não existe}

b)(2×-4)²=0

(2×-4)(2×-4)=0

4ײ-8×-8×+16=0

4ײ-16×+16=0 (:4)

ײ-4×+4=0

∆=16-16

∆=0

×=4±0/2

×=4/2

×=2

S={2}

c)(×-3)²=-2ײ

(×-3)(×-3)=-2ײ

ײ-3×-3×+9=-2ײ

2ײ+ײ-6×+9=0

3ײ-6×+9=0 (:3)

ײ-2×+3=0

∆=4-12

∆=-8

S={não existe}

d)×(×-5)=-6

ײ-5×+6=0

∆=25-24

∆=1

×=5±1/2

×′=5+1/2=6/2=3

×″=5-1/2=4/2=2

S={3;2}

e)×(3×+4)=-1

3ײ+4×+1=0

∆=16-12

∆=4

×=-4±4/6

×′=0

×″=-8/6=-4/3

S={0;4/3}

Fórmulas utilizadas:

∆=b²-4ac

×=-b±√∆/2a

Answer 2

Resposta:

a)(3×+1)²=0

3×+2+1=1

3×+2+0=0

♡=+2×+0=3×

♡=4-9>♡=5

×¹=-2+‐3/2>×¹-2-3/2=-5/2>×¹=-2

ײ=-2+3/2=1/2=ײ=1