Question

Ecuaciones Cuadráticas:
1. 90=(x+1)(90-x/x).
2. 9(3-x)=2x al cuadrado.
3. 2x(x-5)=x+3.

Answer 1

1) 90 = (X + 1)(90 - X/X)

90 = (X + 1)(90 - 1)

90 = (X + 1)(89)

90 = 89X + 89

90 - 89 = 89X

1 = 89X

X = 1/89

2) 9(3 - X) = 2X²

27 - 9X = 2X²

0 = 2X² + 9X - 27

Donde: a = 2; b = 9; c = -27

$X=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$X=\frac{-9\pm \sqrt{9^2-4(2)(-27)}}{2(2)}$

$X=\frac{-9\pm \sqrt{81+216}}{4}$

$X=\frac{-9\pm \sqrt{297}}{4}$

$X=\frac{-9\pm 3\sqrt{33}}{4}$

X1 = [-9 + 3√33]/4 = 2.058421

X2 = [-9 - 3√33]/4 = -6.558421

3) 2X(X - 5) = X + 3

2X² - 10X = X + 3

2X² - 10X - X - 3 = 0

2X² - 11X - 3 = 0

Donde: a = 2;  b = -11;  c = -3

$X=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$X=\frac{-(-11)\pm \sqrt{(-11)^2-4(2)(-3)}}{2(2)}$

$X=\frac{11\pm \sqrt{121+24}}{4}$

$X=\frac{11\pm \sqrt{145}}{4}$

$X=\frac{11\pm \ 12.04159}{4}$

X1 = [11 + 12.04159]/4 = 5.7603975

X2 = [11 - 12.04159]/4 = -0.2603975