Resposta:
Explicació:
# "utilitzant el" color (blau) "llei dels radicals" #
# • color (blanc) (x) sqrtaxxsqrtbhArrsqrt (ab) #
# "utilitzant aquesta llei per simplificar els radicals"
# sqrt12 = sqrt (4xx3) = sqrt4xxsqrt3 = 2sqrt3 #
# sqrt18 = sqrt (9xx2) = sqrt9xxsqrt2 = 3sqrt2 #
# rArr-sqrt12xxsqrt18 #
# = - 2sqrt3xx3sqrt2 #
# = (- 2xx3) xxsqrt3xxsqrt2 #
# = - 6sqrt6 #
Què és (sqrt (5+) sqrt (3)) / (sqrt (3+) sqrt (3+) sqrt (5)) - (sqrt (5-) sqrt (3)) / (sqrt (3+) sqrt (3-) sqrt (5))?
2/7 Prenem, A = (sqrt5 + sqrt3) / (sqrt3 + sqrt3 + sqrt5) - (sqrt5-sqrt3) / (sqrt3 + sqrt3-sqrt5) = (sqrt5 + sqrt3) / (2sqrt3 + sqrt5) - (sqrt5 -sqrt3) / (2sqrt3-sqrt5) = (sqrt5 + sqrt3) / (2sqrt3 + sqrt5) - (sqrt5-sqrt3) / (2sqrt3-sqrt5) = ((sqrt5 + sqrt3) (2sqrt3-sqrt5) - (sqrt5-sqrt3) ) (2sqrt3 + sqrt5)) / ((2sqrt3 + sqrt5) (2sqrt3-sqrt5) = ((2sqrt15-5 + 2 * 3-sqrt15) - (2sqrt15 + 5-2 * 3-sqrt15)) / ((2sqrt3) ^ 2- (sqrt5) ^ 2) = (cancel·lar (2sqrt15) -5 + 2 * 3cancel (-sqrt15) - cancel·lar (2sqrt15) -5 + 2 * 3 + cancel·lar (sqrt15)) / (12-5) = ( -10 + 12) / 7 = 2/7 Tingueu en compte que si en els denomina
Com simplifiqueu (1 / sqrt (a-1) + sqrt (a + 1)) / (1 / sqrt (a + 1) -1 / sqrt (a-1)) div sqrt (a + 1) / (( (a-1) sqrt (a + 1) - (a + 1) sqrt (a-1)), a> 1?
Formatatge matemàtic enorme ...> color (blau) (((1 / sqrt (a-1) + sqrt (a + 1)) / (1 / sqrt (a + 1) -1 / sqrt (a-1)) ) / (sqrt (a + 1) / ((a-1) sqrt (a + 1) - (a + 1) sqrt (a-1))) = color (vermell) (((1 / sqrt (a- 1) + sqrt (a + 1)) / ((sqrt (a-1) -sqrt (a + 1)) / (sqrt (a + 1) cdot sqrt (a-1)))) / (sqrt (a +1) / (sqrt (a-1) cdot sqrt (a-1) cdot sqrt (a + 1) -sqrt (a + 1) cdot sqrt (a + 1) sqrt (a-1))) = color ( blau) (((1 / sqrt (a-1) + sqrt (a + 1)) / ((sqrt (a-1) -sqrt (a + 1)) / (sqrt (a + 1) cdot sqrt (a -1)))) / (sqrt (a + 1) / (sqrt (a + 1) cdot sqrt (a-1) (sqrt (a-1) -sqrt (a + 1))) = color (vermell) ((1 /
Simplifiqueu l’expressió ?: 1 / (sqrt (144) + sqrt (145)) + 1 / (sqrt (145) + sqrt (146)) + ... + 1 / (sqrt (168) + sqrt (169))
1 Primer nota que: 1 / (sqrt (n + 1) + sqrt (n)) = (sqrt (n + 1) -sqrt (n)) / ((sqrt (n + 1) + sqrt (n)) ( sqrt (n + 1) -sqrt (n)) color (blanc) (1 / (sqrt (n + 1) + sqrt (n))) = (sqrt (n + 1) -sqrt (n)) / ((( n + 1) -n) color (blanc) (1 / (sqrt (n + 1) + sqrt (n)) = sqrt (n + 1) -sqrt (n) So: 1 / (sqrt (144) + sqrt (145)) + 1 / (sqrt (145) + sqrt (146)) + ... + 1 / (sqrt (168) + sqrt (169)) = (sqrt (145) -sqrt (144)) + (sqrt (146) -sqrt (145)) + ... + (sqrt (169) -sqrt (168)) = sqrt (169) -sqrt (144) = 13-12 = 1