1 1 ---------------- = ------------------ = Zgodnie ze znaną zasadą mnożymy licznik i mianownik √2 + √3 - 1 √2 + (√3 -1) przez różnicę √2 - (√3-1) , aby skorzystać ze wzoru na różnicę kwadratów: (a+b)(a-b) = a² -b². √2 - (√3-1) √2 - √3 +1 √2 - √3 + 1 = ----------------------------------------------- = ---------------------------- = ------------------------------------ = [ √2+(√3-1)] [ √2- (√3-1)] (√2)² - (√3-1)² 2 - (3 - 2√3 + 1) √2 -√3 +1 √2 - √3 + 1 (√2-√3+1) ( 2√3 + 2) = ------------------------------------ = ---------------------- = --------------------------------------------- = 2 - 4 + 2√3 2√3 - 2 (2√3 - 2) ( 2√3 + 2) 2√6 +2√2 -6 -2√3 +2√3 +2 2√6 +2√2 + √3 -4 2√6 + 2√2 +√3 - 4 = ------------------------------------------------- = ------------------------------------ = ----------------------------- (2√3)² - 2² 12 - 4 8 2 2 2 · [ (1-√2) - √3 ] ------------------ = --------------------- = ----------------------------------------------- = 1 - √2 + √3 (1-√2) + √3 [ (1-√2) +√3] [ (1-√2) - √3] 2 - 2√2 - 2√3 2( 1- √2 - √3) 2(1 - √2 - √3) = ----------------------------------- = ----------------------------- = ------------------------------ = (1-√2)² - (√3)² 1 - 2√2 +2 - 3 -2√2 - (1 - √2 - √3) -√2 (1 - √2 - √3) -√2 + 2 + √6 = ----------------------------- = --------------------------- = ------------------------ √2 √2 · √2 2
