Question

usando o teorema de pitagoras, determine o valor de x

Answer 1

1) x2 = ( 5 ) 2 + ( 12 ) 2
x2 = 25 + 144
x2 = 169
x = √169
x = 13

2) ( x + 9 ) 2 = ( x + 3 ) 2 + ( 2x ) 2
x2+ 18x + 81 = x2 + 6x + 9 + 4x2
x2 - x2 - 4x2 + 18x - 6x + 81 - 9 = 0
- 4x2 + 12x + 72 = 0 ( dividir por -4 )
x2 - 3x - 18 = 0
∆ = 9 + 72
∆ = 81
x = ( 3 + 9 ) /2
x = 12 / 2
x = 6

3) x2 = ( √10 ) 2 + ( 2√2 ) 2
x2 = 10 + 8
x2 = 18
x = √18
x = 3√2

Answer 2

Vamos lá :

a)

x² = 5² + 12²
x² = 25 + 144
x² = 169
x =  √169
x =  13

b)
(x + 9)² = (2x)² + (x + 3)²
x² + 18x + 81 = 4x² + x² + 6x + 9

4x² + 6x + 9 = 18x + 81
4x² + 6x - 18x + 9 - 81 = 0
4x² - 12x - 72 = 0 : 4

x² - 3x - 18 = 0

a = 1 ; b = - 3 ; c = - 18

Δ = 9 + 72
Δ = 81        ⇔⇔√Δ   = 9

x = 3 ± 9/2

x' = 12/2 = 6

c)

x² = (2√2)² + (√10)²
x² = 8 + 10
x² = 18
x = √18
x = 3√2


Espero ter ajudado !!!!