Question

Rezolvati in R ecuatiile
a.ײ-1=24
b.(5×-1)²=36
c.(2-3×)²=-4

Answer 1

Răspuns:

Explicație pas cu pas:

a)

x² - 1 = 24

x² = 24 + 1

x² = 25 =>  x = ±√25 =>   x = ± 5 ∈ R

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b)

( 5 x - 1)² = 36

( 5 x - 1)² =(± 6)²

5 x - 1 = ± 6 =>   x = (6+1)/5 =>  x = 7/5

                           x = (-6+1)/5 =>   x = - 1

Sau:

25 x² - 10 x + 1 = 36

25 x² - 10 x - 35 = 0   [ : 5

5 x - 2 x - 7 = 0

Δ = 4 + 140 = 144

x = ( 2±√144)/(2×5) = (2±12)/10 => x = 14/10 = 7/5

                                                          x = -10/10 = - 1

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c)

(2-3x)² = 4   ( Orice numar ridicat la patrat da un numar pozitiv)

(2 - 3 x)² = (±2)²

2 - 3 x = 2

- 3 x = 2 - 2

x = 0

2 - 3 x = - 2

-  3 x = - 2 - 2

x = 4/3  

sau:

4 - 12 x + 9 x² = 4

9 x² - 12 x = 4 - 4

3 x ( 3 x - 4 ) = 0

3 x = 0 =>   x = 0

3 x - 4 = 0 =>   x = 4/3