Question

Calcule o valor de x nos triângulo retângulo 2x x-3 x-9

Answer 1

2x ; x - 3 ; x - 9

(2x)^2 = (x - 3)^2 + (x - 9)^2

4x^2 = [(x)^2 - 2(x)(3) + (3)^2 ] + [(x)^2 - 2(x)(9) + (9)^2

4x^2 = x^2 - 6x + 9 + x^2 - 18x + 81

4x^2 = 2x^2 - 24x + 90

4x^2 - 2x^2 + 34x - 90 = 0

2x^2 + 34x - 90 = 0

a=2. b= 35 c = - 90

D = b^2 - 4 a c

D = (34)^2 - 4(2)(-90)

D = 1.156 - 8 (-90)

D = 1.156 - 720

D = 436

X = - b -,+ \/D
......._______
......... ....2a

X - (-34) - , + \/436
......___________
............2x2

X = 34 - , + 20,88
.......__________
...................4

x1 = 34 - 20,88
......._________
..................4

X1 = 13,12
.........____
..............4

X1 = 3,28


X2 = 34 + 20,88
........._________
................. ..4

X2 = 54,88
........._____
..............4

X^2 = 13,72