[8.25-0.5^-0.5(2^-0.5+4^-0.25)]^1/2
proszę też o wytłumaczenie jak policzyć te potęgi
Dla osób nie mogących się rozczytać zadanie w załączniku!
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.....= [ 8,25 - (1/2)^(-1/2) * ((1/2)^(1/2) + (1/4)^(1/4)) ]^(1/2) =
[ 8,25 - 2^(1/2) * ( √(1/2) + ((1/4)^(1/2))^(1/2) ]^(1/2) =
[ 8,25 - √2 * (√2/2 + (√(1/4))^(1/2) ]^(1/2) =
[8,25 - √2 * (√2/2 + (1/2)^(1/2) ]^(1/2) = [8,25 - √2 * (√2/2 + √(1/2) ]^(1/2) =
[8,25 - √2 * (√2/2 + √2/2)]^(1/2) = [8,25 - √2 * 2 * √2/2 ]^(1/2) =
[ 8,25 - √2 * √2 ]^(1/2) = [ 8,25 - 2 ]^(1/2) = (6,25)^(1/2) = √6,25 = 2,5