Sederhanakan bentuk a^(2)−b^(2) untuk a=1/(3-2√2) dan b=1/(3+2√2)

Jawaban 24√2 Konsep! * Rasionalkan akar dengan kali akar sekawan dari penyebutnya. * √a² = a * a√b × √c = a√(b × c) * a² – b² = (a – b)(a + b) * (a – b)² = a² – 2ab + b² * (a + b)² = a² + 2ab + b² Pembahasan: a² = (1/(3 – 2√2))² = 1²/(3 – 2√2)² = 1/(3² – 2.3.2√2 + 2²√2²) = 1/(9 – 12√2 + 4.2) = 1/(9 – 12√2 + 8) = 1/(17 – 12√2) Rasionalkan (1/(17 – 12√2)) × ((17 + 12√2)/(17 + 12√2)) = (17 + 12√2)/((17 – 12√2)(17 + 12√2)) = (17 + 12√2)/(17² – 12²√2²) = (17 + 12√2)/(289 – 144.2) = (17 + 12√2)/(289 – 288) = (17 + 12√2)/1 = 17 + 12√2 b² = = (1/(3 + 2√2))² = 1²/(3 + 2√2)² = 1/(3² + 2.3.2√2 + 2²√2²) = 1/(9 + 12√2 + 4.2) = 1/(9 + 12√2 + 8) = 1/(17 + 12√2) Rasionalkan (1/(17 + 12√2)) × ((17 – 12√2)/(17 – 12√2)) = (17 – 12√2)/((17 + 12√2)(17 – 12√2)) = (17 – 12√2)/(17² – 12²√2²) = (17 – 12√2)/(289 – 144.2) = (17 – 12√2)/(289 – 288) = (17 – 12√2)/1 = 17 – 12√2 Maka, a² – b² = 17 + 12√2 – (17 – 12√2) = 17 + 12√2 – 17 + 12√2 = 17 – 17 + 12√2 + 12√2 = (12 + 12)√2 = 24√2 Jadi, hasilnya adalah 24√2.