Question

Encontre o "X" :
Me ajudem

Answer 1

Pitágoras:
H^2 = a^2 + b^2

a)
(5√2)^2 = 4^2 + x^2
25.2 = 16 + x^2
50-16 = x^2
34 = x^2
x^2 = 34
x = +/- √34
R.: x = √34

B)
(x+2)^2 = 3^2 + 5^2
x^2 + 2.2x + 4 = 9 + 25
x^2 + 4x + 4 = 34
x^2 + 4x + 4 - 34 = 0
x^2 + 4x - 30 = 0
a= 1; b = 4; c = - 30
∆ = b^2-4ac
∆ = 4^2 - 4.1.(-30)
∆ = 16+120
∆ = 136
√∆ = √136 = √4.√34 = 2√34
x = [ - b +/- √∆]/2a
x = [ - 4 +/- 2√34]/2.1
x = [- 4 +/- 2√34]/ 2
x = [- 4/2 +/- 2√34]/2
x' = [- 2 + √34] (sim)
x" = [- 2 - √34] (descarte)
R.: x = - 2 + √34

C)
9^2 = 4^2 + (x-3)^2
81 = 16 + x^2 - 2.3x + 9
81 = 25 + x^2 - 6x
0 = x^2 - 6x + 25 - 81
0 = x^2 - 6x - 56
x^2 - 6x - 56 = 0
a= 1; b = - 6; c = - 56
∆ = b^2-4ac
∆ = (-6)^2 - 4.1.(-56)
∆ = 36 + 224
∆ = 260
√∆ = √4.√65 = 2√65
x = [ - b +/- √∆]/2a
x = [ -(-6)+/- 2√65]/2.1
x = [6 +/- 2√65]/2
x = 3 + √65 (sim)
x = 3 - √65 (descarte)
R.: x = 3 + √65