Oblicz:a) b)
a)
.... = √[ √(13 + 2) * √(13 - 2) = √( √15 * √11) = √(√165) = √(165^(1/2)) = [165^(1/2)]^(1/2) = 165^(1/2 * 1/2) = 165^(1/4) = ⁴√165
b)
... = 1 / (1 - √2) * 1 / (1 + √2) = (1 * 1) / [ ( 1 - √2)(1 +√2)] = 1 / (1 - 2) = 1/ (-1) = -1
√√(13+2) · √√13-2) = √√(169-4) = √√165 = (165¹/₂)¹/₂ = ⁴√165
1 1 1 1
-------- · -------- = -------- = ------ = -1
1-√2 1+√2 1-2 -1
(a-b)(a+b) = a²-b²
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a)
.... = √[ √(13 + 2) * √(13 - 2) = √( √15 * √11) = √(√165) = √(165^(1/2)) = [165^(1/2)]^(1/2) = 165^(1/2 * 1/2) = 165^(1/4) = ⁴√165
b)
... = 1 / (1 - √2) * 1 / (1 + √2) = (1 * 1) / [ ( 1 - √2)(1 +√2)] = 1 / (1 - 2) = 1/ (-1) = -1
a)
√√(13+2) · √√13-2) = √√(169-4) = √√165 = (165¹/₂)¹/₂ = ⁴√165
b)
1 1 1 1
-------- · -------- = -------- = ------ = -1
1-√2 1+√2 1-2 -1
(a-b)(a+b) = a²-b²