Odpowiedź:
a)
(x + 3)(x + 5) = - 4 (x² + 2) + 5x²
x² + 5x + 3x + 15 = - 4x²- 8 + 5x²
x² + 4x² - 5x² + 5x + 3x = - 8 - 15
8x = - 23 /: 8
x = - 23/8
spr.
L = (x + 3)(x + 5) = (-23/8 + 3) (- 23/8 + 5) = (- 23/8 + 24/8)(- 23/8 + 40/8)=
= 1/8 * 17/8 = 17/64
P = - 4 (x² + 2) + 5 * (-23/8)²= - 4((- 23/8)² + 2) + 5* (- 23/8)² =
= - 4 (529/64 + 128/64) + 5 * (529/64)= - 4 * 657/64 + 2645/64 =
= - 2628/64 + 2645/64 = 17/64
L = P
b)
(x - 2) (x + 4) = x(x - 5)
x² + 4x - 2x - 8 = x²- 5x
x² - x² + 4x - 2x + 5x = 8
7x = 8 / : 7
x = 8/7
spr.
L = (x - 2)(x + 4) = (8/7 - 2)(8/7 + 4) = (8/7 - 14/7)(8/7 + 28/7) =
= - 6/7 * 36/7 = - 216/49 = - 4 20/49
P = x(x - 5) = 8/7(8/7 - 5) = 8/7 * (8/7 - 35/7) = 8/7 * (- 27/7) =
= - 216/49 = - 4 20/49
L = P
c)
- 2x (x + 1) = (3 - 2x)(x + 2)
- 2x² - 2x = 3x + 6 - 2x²- 4x
- 2x² + 2x² - 2x - 3x + 4x = 6
- x = 6 / (- 1)
x = - 6
spr.
L = - 2x (x + 1) = - 2 *(- 6) *(- 6 + 1) = 12 * (-5) = - 60
P = (3 - 2x)(x + 2) = (3 - 2 * (- 6))(- 6 + 2) = (3 + 12) * (- 4) = 15 * (-4) = - 60
L = P
d)
(x - 3)(x + 3) = (x - 2)²
x² + 3x - 3x - 9 = x² - 2x - 2x + 4
x² - x² + 3x - 3x + 2x + 2x = 4 + 9
4x = 13 / : 4
x = 13/4
spr.
L = (x - 3)(x + 3) = (13/4 - 12/4)(13/4 + 12/4) = 1/4 * 25/4 = 25/16 = 1 9/16
P = (x - 2)² = (13/4 - 8/4)² = (5/4)² = 25/16 = 1 9/16
L = P
Szczegółowe wyjaśnienie:
