Oblicz:
[(5²⁰ - 5¹⁸ √2): (√2)⁷· 5¹⁸]: 16·5⁻³
[(5²⁰ - 5¹⁸ √2): (√2)⁷· 5¹⁸]: 16·5⁻³=
5²⁰ - 5¹⁸ √2 5¹⁸(5²-√2) 5²-√2
--------------- :16·5⁻³ = ---------------- :16·1/5³ = ----------:16·1/5³ =
(√2)⁷· 5¹⁸ (√2)⁷·5¹⁸ √(2)⁷
5²-√2 5²-√2 16 5²-√2 5³ 5³(5²-√2) 5⁵-5³√2
-------- = ------------- :------- = ---------- · ------ = ------------- = ----------- =
√128 √2·√64 5³ 8√2 16 16·8√2 64√2
(5⁵-5³√2)·64√2 = 5⁵·64√2 - 5³√2·64√2 = 3125·64√2 - 125·64·√4 =
= 200000√2-16000 lub można zapisać tak (200√2-16)·10³
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[(5²⁰ - 5¹⁸ √2): (√2)⁷· 5¹⁸]: 16·5⁻³=
5²⁰ - 5¹⁸ √2 5¹⁸(5²-√2) 5²-√2
--------------- :16·5⁻³ = ---------------- :16·1/5³ = ----------:16·1/5³ =
(√2)⁷· 5¹⁸ (√2)⁷·5¹⁸ √(2)⁷
5²-√2 5²-√2 16 5²-√2 5³ 5³(5²-√2) 5⁵-5³√2
-------- = ------------- :------- = ---------- · ------ = ------------- = ----------- =
√128 √2·√64 5³ 8√2 16 16·8√2 64√2
(5⁵-5³√2)·64√2 = 5⁵·64√2 - 5³√2·64√2 = 3125·64√2 - 125·64·√4 =
= 200000√2-16000 lub można zapisać tak (200√2-16)·10³