(3 +) sqrt (5)) - (sqrt) (5) sqrt (3)) / (sqrt (3 +) sqrt (3) sqrt (5))?
(Sqrt3 + sqrt3) / (sqrt3 + sqrt3-sqrt5) = (sqrt5 + sqrt3) / (2sqrt3 + sqrt5) - (sqrt5 + sqrt3) / (sqrt3 + sqrt3) (sqrt5-sqrt3) / (2sqrt3-sqrt5) = ((sqrt5 + sqrt3) (2sqrt3-sqrt5) - (sqrt5-sqrt3) (sqrt5-sqrt3) ) (2sqrt3 + sqrt5) / ((2sqrt15 + 5-2 * 3-sqrt15)) ((2sqrt3-5 + 2 * 3-sqrt15) (2) * (2) * (2) * (2) * (+) 2 (3) * ביטול (2) 10 +) = 7 = 2/7 שים לב שאם במכנה הם (sqrt3 + sqrt (3 + sqrt5) ו (sqrt3 + sqrt (3-sqrt5)) אז התשובה תהיה שינוי.
איך אתה מפשט (1 / sqrt (a-1) + sqrt (a + 1)) / (1 / sqrt (a + 1) -1 / sqrt (a-1)) div sqrt (a + 1) / (א 1) - (a + 1) sqrt (a-1)), a> 1?
(1 + sqrt (a-1) + sqrt (a + 1)) / (1 / sqrt (a + 1) -1 / sqrt (a-1) ) (1 +) (1 +) - (1 +) - (1 +) - (1 +) sqrt (a - 1)) (= צבע = אדום) ((1 / sqrt (a- 1) +) (1 +)) / ((1) sqrt (a-1) -qqrt (a 1)) / (sqrt (a + 1) cdot sqrt (a-1)))) / (sqrt (1 +) cdot sqrt (a + 1) sqrt (a-1)) = צבע = (1) (1) / sqrt (a-1) + sqrt (a + 1)) / ((sqrt (a-1) -qqrt (a + 1)) / (sqrt (a + 1) cdot sqrt ) 1 () 1 () 1 () 1 () 1 () 1 () 1 () 1 () 1 () = 1) (1) / sqrt (a-1) + sqrt (a + 1)) / ((sqrt (a-1) -qqrt (a + 1)) / (sqrt (a + 1) cdot sqrt (a-1) ) (x 1) sqx (1 +) cdot sqrt (a-1) (sqrt (a-1) -qqrt (a + 1))) / sqrt (+ 1) = צבע (כחול) (1 / sqrt (a-1) +) (x
לפשט את הביטוי ?: 1 / (sqrt (144) + sqrt (145)) + 1 / (sqrt) (145) + sqrt (146)) + + 1 / (sqrt (168) + sqrt (169))
1 (1) (1) (sq + n) 1 (+ 1) + sqrt (n)) = (n = 1) - nq) (n + 1) -qqrt (n)) צבע (לבן) (1 / (sqrt (n + 1) + sqrt (n)) = (sqt (n + 1) - sqrt (n)) / ( (n + 1) - n (1) (1) (1) (sq + n) 1 + sqrt (n)) = sqrt (n + 1) - sqrt (n) אז: 1 / (sqrt (144) + (+) (1) (1) (1) (1) (1) (1) (1) (1) (1) (146) - sqrt (169) -sqrt (144) = 13-12 = 1