1)
5x(5x + 2) + 3 = 2
25x² + 10x + 3 - 2 = 0
25x² + 10x + 1 = 0
[tex] x_{12} = \frac{-b \pm \sqrt{ b^{2}-4ac}}{2a}= \\ \\ =\frac{-10 \pm \sqrt{ 10^{2}-4*25*1}}{2*25}= \\ \\ =\frac{-10 \pm \sqrt{ 100-100}}{50}= \\ \\ =\frac{-10 \pm \sqrt{ 0}}{50}=\frac{-10}{50}=\frac{-1}{5} \\ \\ x_{1}=x_{2} = \boxed{\frac{-1}{5} }[/tex]
2)
64 - x² = 0 | * (-1)
x² - 64 = 0
x² = 64
[tex]x = \pm \sqrt{64} \\ x_1 = \boxed{8} \\ x_2 = \boxed{-8}[/tex]
3)
[tex] \sqrt{3}x^{2}=0 \\ x_1 = x_2 = \boxed{0} [/tex]
"4")
2x² - x - 1 = 2x² - 2x + x - 1 = 2x(x - 1) + (x - 1) = (x - 1)(2x + 1)
Din imagine:
1)
x(x+4)=21
x² + 4x - 21 = 0
x² - 3x + 3x + 4x - 21 = 0
x² - 3x + 7x - 21 = 0
x(x - 3) + 7(x - 3) = 0
(x - 3)(x + 7) = 0
x1 = 3
x2 = - 7 (Aceasta solutie va fi eliminata deoarece latura dreptunghiului nu poate fi negativa)
=> x = 3 cm
l = x = 3 cm
L = x + 4 = 3 + 4 = 7 cm
Proba: A L * l = 7 * 3 = 21 cm²
2)
x(x + 1) = 30
x² + x - 30 = 0
x² - 5x + 5x + x - 30 = 0
x² - 5x + 6x - 30 = 0
x(x - 5) + 6(x - 5) = 0
(x - 5)(x + 6) = 0
x1 = 5
x2 = - 6 (Aceasta solutie o eliminam deoarece o latura a unui patrat nu poate fi negativa)
=> x = 5 cm
l = x = 5 cm
L = x + 1 = 5 + 1 = 6 cm
Proba: A = L * l = 6 * 5 = 30 cm²
