Question

Rozwiąż równania :

Answer 1

a)

(√7-√3x)(√7+√3x)=0

√7=√3x v √3x=-√7

x=√(7/3) v x= - √(7/3)

b)

9x²+98=0  brak rozw. Δ<0

c)

x²+6=0 brak. rozw.

d)

Δ=16-16=0

x=4/4√2=√2/2

e)

Δ=3-8=-5 brak rozw.

f)

9x²+x-16=0

Δ=1+36*16=577

 

x₁= (-1-√577)/18; x₂= (-1+√577)/18

g)

Δ=32

√Δ=4√2

x=4-4√2 v x=4+4√2

h)

(1-√3/2x)(1+√3/2x)=0

x=2√3/3 v x= -2√3/3

i)

25(4x²-1)=0

(2x-1)(2x+1)=0

x=1/2 v x= -1/2

Answer 2

a)

- 3 x^2 + 7 = 0

3 x^2  = 7

x^2 = 7/3

x = - p(7/3)  lub  x = p(7/3)

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b)

- 49 = 9 x^2 + 49

9 x^2 = - 98

x^2 = - 98/9   - sprzeczność - nie ma rozwiązania

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c) 2 x^2 = - 6

x^2 = - 3  - sprzeczność - nie ma rozwiązania

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d)

2 p(2) x^2 - 4 x + p(2) = 0

delta = (-4)^2 - 4*2 p(2)*p(2) = 16 - 16 = 0

x = 4/( 4 p(2)] = 1/p(2) = p(2)/2

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e)

- 2 x^2 - p(3) x - 1 = 0

delta = [ - p(3)]^2 - 4*(-2)*(-1) = 3 - 8 = - 5 < 0

Nie ma pierwiastków

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f)

9 x^2 - 16 = - x

9 x^2 + x - 16 = 0

delta = 1^2 - 4*9*(-16) = 1 + 576 = 577

x = [ -1 - p(577)]/18    lub   x = [ -1 + p(577)]/18

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g)

(1/2) x^2 - 4 x - 8 = 0

delta = (-4)^2 - 4*(1/2)*(-8) = 16 + 16 = 32

p(delty) = p(16*2) = 4 p(2)

x = [ 4  - 4 p(2)]/[2*(1/2)] = 4 - 4 p(2)   lub  x = [ 4 + 4 p(2)]

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h)

( -3/4) x^2 + 1 = 0

(3/4) x^2 = 1    / * 94/3)

x^2 = 4/3

x = - p(4/3)   lub  x = p(4/3)

x = - 2/p(3)   lub   x = 2/p(3)

x = ( -2/3)p(3)    lub  x = (2/3) p(3)

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i)

100 x^2 - 25 = 0

100 x^2 = 25   / : 100

x^2 = 25/100 = 1/4

x = - 1/2  lub  x = 1/2

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