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Što je (sqrt (5+) sqrt (3)) / (sqrt (3+) sqrt (3+) sqrt (5)) - (sqrt (5-) sqrt (3)) / (sqrt (3+) sqrt) (3) sqrt (5))?
2/7 Primamo, 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) (2sqrt3 + sqrt5) / ((2sqrt15-5 + 2 * 3-sqrt15) - (2sqrt15 + 5-2 * 3-sqrt15)) / ((2sqrt3) ^ 2- (sqrt5) ^ 2) = (poništi (2sqrt15) -5 + 2 * 3kkazati (-sqrt15) - otkazati (2sqrt15) -5 + 2 * 3 + otkazati (sqrt15)) / (12-5) = ( Imajte na umu da, ako su u nazivnicima (sqrt3 + sqrt (3 + sqrt5)) i (sqrt3 + sqrt (3-sqrt5)), odgovor će biti promijenjen.
Kako pojednostavnite sqrt (x-1) + sqrt (2x) = 3?
Rarrx = 2 rarrsqrt (x-1) + sqrt (2x) = 3 rarrsqrt (x-1) = 3-sqrt (2x) rarr [sqrt (x-1)] ^ 2 = [3-sqrt (2x)] ^ 2 rarrx-1 = 9-6sqrt (2x) + 2x rarr6sqrt (2x) = x + 10 rarr [6sqrt (2x)] ^ 2 = [x + 10] ^ 2 rarr36 * (2x) = x ^ 2 + 20x + 100 rarrx ^ 2-52x + 100 = 0 rarrx ^ 2-2 * x * 26 + 26 ^ 2-26 ^ 2 + 100 = 0 rarr (x-26) ^ 2 = 26 ^ 2-100 = 576 rarrx-26 = sqrt (576) = + - 24 rarrx = 26 + 24,26-24 = 50 ili 2 Stavljanje x = 50 u zadanu jednadžbu, dobivamo, rarrsqrt (50-1) + sqrt (2 * 50) = 17 (odbijeno) ) Stavljanje x = 2 u zadanu jednadžbu, dobivamo, rarrsqrt (2-1) + sqrt (2 * 2) = 3 (prihvaćeno) Dakle, tražena vrijednost x je 2.
(sqrt 5 - sqrt 7) (sqrt 5 - sqrt 8) Pomnožite i pojednostavnite?
(sqrt5-sqrt7) (sqrt5-sqrt8) = boja (plava) (5-2sqrt10-sqrt35 + 2sqrt14 (sqrt5-sqrt7) (sqrt5-sqrt8) Koristite metodu FOIL. http://en.wikipedia.org/wiki/ FOIL_method (sqrt5sqrt5) - (sqrt5sqrt8) - (sqrt5sqrt7) + (sqrt7sqrt8) Pojednostavite. 5-sqrt40-sqrt35 + sqrt56 Prime faktorizira radikande. 5-sqrt (2 * 2 * 2 * 5) -sqrt (5 * 7) + sqrt (2 * 2 * 2 * 7) Pojednostavite. 5-2sqrt10-sqrt35 + 2sqrt14