Determine o valor do numero x em cada uma das igualdades a)14V28=xV24 b)15V105= 3V10x c) 8V54=V5x d) 10V6x=5V6
Respostas
Resposta:
a) 14√28=x√24
=> 14√2²7 = x√2²6
=> 14√2²√7 = x√2²√6
=> 14.2√7 = x2√6
=> 28√7 = x2√6
=> 28√7 = 2√6x
=> 2√6x = 28√7
=> x= 28√7
2√6
=> x= 14√7
√6
=> x= 14√7 × √6
√6 √6
=> x= 14√7√6
√6√6
=> x= 14√42
√36
=> x= 14√42
6
=> x= 7√42
3
b) 15√105 = 3√10x
3√10x = 15√105
=> x= 15√105
3√10
=> x= 5√105
√10
=> x= 5√21
√2
=> x= 5√21 × √2
√2 √2
=> x= 5√21√2
√2√2
=> x= 5√42
√4
=> x= 5√42
2
c) 8√54=√5x
=> 8√3²×6 = √5x
=> 8√3²√6 = √5x
=> 8×3√6 = √5x
=> 24√6 = √5x
=> √5x = 24√6
=> x= 24√6
√5
=> x= 24√6 × √5
√5 √5
=> x= 24√6√5
√5√5
=> x= 24√30
√25
=> x= 24√30
5
d) 10√6x=5√6
=> x= 5√6
10√6
=> x= 5×1
10
=> x= 5
10
=> x= 1
2
Espero ter ajudado!!
:)