Respuestas
Respuesta:
I) x = 8.66
II) x = 2.28
III) x = 3
Explicación paso a paso:
I)
Triangulo rectángulo:
Cateto 1 = x
Cateto 2 = 15 - 10 = 5
Hipotenusa = 10
Utilizar teorema de pitagoras:
10² = x² + 5²
100 = x² + 25
100 - 25 = x²
75 = x²
√75 = x₁
x₁ = √75
x₁ = 8.66, si
- √75 = x₂
x₂ = - √75
x₂ = - 8.66, no
x = 8.66
II)
Triangulo rectángulo:
Cateto 1 = 6
Cateto 2 = x + 1
Hipotenusa = 3x
Utilizar teorema de pitagoras:
(3x)² = 6² + (x + 1)²
9x² = 36 + x² + 2x + 1
9x² - 36 - x² - 2x - 1 = 0
8x² - 2x - 37 = 0
x₁ = [-(- 2) + √((- 2)² - 4(8)(- 37))] / [2(8)]
x₁ = [2 + √(4 + 32(37))] / 16
x₁ = [2 + √(4 + 1184)] / 16
x₁ = [2 + √1188] / 16
x₁ = [2 + 34.4674] / 16
x₁ = 36.4674 / 16
x₁ = 2.2792
x₁ = 2.28, si
x₂ = [-(- 2) - √((- 2)² - 4(8)(- 37))] / [2(8)]
x₂ = [2 - √(4 + 32(37))] / 16
x₂ = [2 - √(4 + 1184)] / 16
x₂ = [2 - √1188] / 16
x₂ = [2 - 34.4674] / 16
x₂ = - 32.4674 / 16
x₂ = - 2.0292
x₂ = - 2.03, no
x = 2.28
III)
Triangulo rectángulo:
Cateto 1 = x
Cateto 2 = x + 1
Hipotenusa = x + 2
Utilizar teorema de pitagoras:
(x + 2)² = x² + (x + 1)²
x² + 4x + 4 = x² + x² + 2x + 1
0 = x² + x² + 2x + 1 - x² - 4x - 4
0 = x² - 2x - 3
x² - 2x - 3 = 0
x - 3 -------> - 3x
x + 1 -------> x
- 2x
(x - 3)(x + 1) = 0
x - 3 = 0
x₁ = 3, si
x + 1 = 0
x₂ = - 1, no
x = 3