Д)
х - 2 = 15/х | × x
х≠0
х(х - 2) = 15
x² - 2x = 15
x² - 2x - 15 = 0
D= (-2)² - 4×1×(-15) = 4 + 60 = 64 = 8²
D>0
x₁ = ( - (-2) - 8) / (2×1) = (2 - 8)/2 = -6/2 = -3
x₂ = ( - (-2) + 8) / (2×1) = (2 + 8)/2 = 10/2 = 5
Проверим:
- 3 - 2 = 15/(-3)
- 5 = - 5
5 - 2 = 15/5
3 = 3
Ответ: х₁ = - 3 ; х₂ = 5.
ж)
3х - (8/х) = 10 |×x
x≠0
3x² - 8 = 10x
3x² - 10x - 8 = 0
D = (-10)² - 4×3×(-8) = 100 + 96 = 196 = 14²
D>0
x₁ = ( - ( - 10) - 14) / (2 × 3) = ( 10 - 14)/6 = -4/6 = - 2/3
x₂ = ( - (- 10) + 14) / (2× 3) = ( 10 + 14)/6 = 24/6 = 4
Проверим:
3 × ( - 2/3) - 8 / ( - 2/3) = 10
- 2 - (8/1) × ( - 3/2) = 10
- 2 + 12 =10
10=10
3×4 - (8/4) = 10
12 - 2 = 10
10 = 10
Ответ: х₁ = - 2/3 ; х₂ = 4