va rog sa ma ajutati.dau coroana
Răspunsuri la întrebare
Ex. 1 3x²-147=0 3x²=147 x²=147/3 = 49
x=±√49 x=±7 ⇒ x₁=7 x₂= - 7
Ex. 2 49 = 16
45 5x² la ex.2 facem produs mezi egal
cu produs extremi (inmultire pe diagonala)
49·5·x² = 16·45 245x² = 720
720 ⁽⁵ 144 144 12
x² = ----------- = --------- ⇒ x₁;₂ = ±√------- = ± -------
245 49 49 7
x₁=12/7 x₂= - 12/7
Ex.3
(2x-7)² = 225 (a-b)²=a²-2ab+b²
2²x² - 2·2·x·7 + 7² = 225
4x² - 28x + 49 - 225 = 0 , x²-7x-44=0
Δ=b² - 4ac = 225
√Δ= √225 = 15
x₁;₂ = [-b±√Δ] / 2a = [7±15] / 2
x₁ = [7+15] / 2 = 11 x₂= [7-15] / 2 = 4
Ex.4
6x² = (√30 - 3√6 )² ; 6x²=30-2·√30·3·√6 +3²·6
6x²= 84 - 6 √180 ; 180=2²·3²·5²
6x²= 84 - 6·6·√5
6x²= 84 - 36·√5 | :6
x² = 14 - 6√5 ; x₁;₂ = ± √ [14 - 6√5]
x₁ = + √ [14 - 6√5]
x₂ = - √ [14 - 6√5]
Ex.5 - 0,192 x² + 0,75 = 0
Vom transforma aceste numere zecimale (fractii zecimale) in fractii ordinare (in numere cu linie de fractie)
0,192 = 192/1000 = 24/125
0,75 = 75/100 = 3/4
24 3
- ------- x² + -------- = 0
125 4
- 24/125 x² = - 3/4 , x² = (3/4) / (24/125)
x² = (3/4) : (24/125) orice fractie este o impartire ascunsa
x² = (3/4) · (125/24) facem simplificare cu 3
x² = 125/32 = (5·5²) / (2·2²·2²)
x₁;₂ = ± √ [ (5·5²) / (2·2²·2²)]
x₁;₂ = ± 5/4 √ 5/2 , x₁;₂ = ± (5/4 ) (√ 5 /√ 2)
rationalizam cu √ 2
x₁;₂ = ± (5√10) / 8
x₁ = + (5√10) / 8
x₂ = - (5√10) / 8
Ex. 6 (3x - 2√3)² = 75 (a-b)²=a²-2ab+b²
9x² - 2·3·x·2·√3 + 2²· 3 = 75
9x² - 12√3 x -63 =0 | :3
3x² - 4√3 x - 21 = 0
Δ=b²- 4ac = 16·3 - 4·3·(-21)=300= 3·2²·5²
√Δ = √3·2²·5² = 10√3
- b ± √Δ 4√3 ± 10√3 ⁽² 2√3 ± 5√3
x₁;₂ = --------------- = ----------------- = ---------------------
2a 2 · 3 3
2√3 + 5√3 7√3
x₁ = --------------- = --------------
3 3
2√3 - 5√3 - 3√3 ⁽³
x₂ = --------------- = -------------- = - √3
3 3