radiciação

por ELIZANGELA MARTINS Ter 14 maio 2013, 19:09

se K=

radiciação FlPrLaqMwVTnSmY6kzBVGcKpjpTMNWZgulf1AGnIVmhN1gAAAAASUVORK5CYII=

, então raiz de 12.( k^2 -2) é: resultado é 6

por PedroCunha Ter 14 maio 2013, 20:00

Vamos lá.

Primeiramente, o seu Tópico vai contra as Regras do Fórum.

Você deve digitar o enunciado sempre que for possível.

Agora, quanto à questão.

Como ele quer saber o valor de radiciação %5CLARGE%5C%21%5Csqrt%7B12%20%5Ccdot%20%28k%5E2-2%29%7D

radiciação %5CLARGE%5C%21%5Csqrt%7B12%20%5Ccdot%20%28k%5E2-2%29%7D

, uma maneira de resolver é elevando toda a expressão dada no enunciado ao quadrado.

Veja:

$radiciação %5CLARGE%5C%21%255CLARGE%255C%2521K%2520%253D%2520%255Csqrt%257B%255Cfrac%257B%255Csqrt6%2520%252B%2520%255Csqrt%25202%257D%257B%255Csqrt6%2520-%2520%255Csqrt%25202%257D%257D%2520%255Ctherefore%2520K%255E2%2520%253D%2520%255Cfrac%257B%255Csqrt6%2520%252B%2520%255Csqrt2%257D%257B%255Csqrt6%2520-%2520%255Csqrt2%257D%2520%255Ctherefore%2520K%255E2%2520%253D%2520%255Cfrac%257B%2528%255Csqrt6%2520%252B%2520%255Csqrt2%2529%2520%255Ccdot%2520%2528%255Csqrt6%2520%252B%2520%255Csqrt2%2529%257D%257B%2528%255Csqrt6%2520-%2520%255Csqrt2%2529%2520%255Ccdot%2520%2528%255Csqrt6%2520%252B%2520%255Csqrt2%2529%257D%2520%255Ctherefore%2520%255C%255C%255C%255C%2520K%255E2%2520%253D%2520%255Cfrac%257B%255Csqrt6%255E2%2520%252B%25202%2520%255Ccdot%2520%255Csqrt%25206%2520%255Ccdot%2520%255Csqrt%25202%2520%252B%2520%255Csqrt2%255E2%257D%257B%255Csqrt6%255E2%2520-%2520%255Csqrt2%255E2%257D%2520%255Ctherefore%2520K%255E2%2520%253D%2520%255Cfrac%257B6%2520%252B%25202%2520%252B%25202%255Csqrt%257B12%257D%257D%257B6%2520-%25202%257D%2520%255Ctherefore%2520K%255E2%2520%253D%2520%255Cfrac%257B8%2520%252B%25202%255Csqrt%257B12%257D%257D%257B4%257D%2520%255Ctherefore%2520%255C%255C%255C%255C%2520K%255E2%2520%253D%2520%255Cfrac%257B2%2520%255Ccdot%2520%25284%2520%252B%2520%255Csqrt%257B12%257D%2529%257D%257B4%257D%2520%255Ctherefore%2520K%255E2%2520%253D%2520%255Cfrac%257B4%2520%252B%2520%255Csqrt%257B12%257D%257D%257B2%257D%20%5Ctherefore%20K%5E2%20%3D%20%5Cfrac%7B4%20%2B%202%5Csqrt%7B2%7D%7D%7B3%7D%20%5Ctherefore%20K%5E2%20%3D%202%20%2B%20%5Csqrt%7B3%7D$

Finalmente, substituindo na expressão procurada:

radiciação %5CLARGE%5C%21%5Ctherefore%20K%5E2%20%3D%202%20%2B%20%5Csqrt%7B3%7D%20%5C%5C%5C%5C%5Csqrt%7B12%7D%20%5Ccdot%20%28%282%20%2B%20%5Csqrt%7B3%7D%20-%202%29%20%5Ctherefore%20%5Csqrt%7B12%7D%20%5Ccdot%20%28%5Csqrt3%29%20%5Ctherefore%20%5Csqrt%7B36%7D%20%5Ctherefore%206