Jika p=(√15) + √3 dan q = (√15) - √3 , tentukan nilai berikut dalam bentuk paling sederhana! c. (2p+q)/3q

<p>Jawab: (4+√5)/3</p><p>Pembahasan:</p><p>Ingat!</p><ul><li>Menyederhanakan bentuk pecahan dengan merasionalkan berarti mengalikan pembilang dan penyebut pecahan dengan bentuk sekawan dari penyebutnya.</li><li>Bentuk sekawan dari (a√b-c√d) adalah (a√b+c√d).&nbsp;</li><li>√a × √b = √(a×b).</li><li>√a × √a = a.</li></ul><p>Dengan menggunakan konsep di atas, diperoleh</p><p>Perhatkan bahwa:</p><p>2p+q = 2(√15+√3)+(√15-√3)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 2√15+2√3+√15-√3</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 3√15+√3</p><p>Dan,&nbsp;</p><p>3q = 3(√15-√3)</p><p>&nbsp; &nbsp; &nbsp; = 3√15-3√3</p><p>Sehingga,</p><p>Bentuk sekawan dari ( 3√15-3√3) adalah ( 3√15+3√3). Maka,</p><p>(2p+q)/3q = (3√15+√3)/(3√15-3√3) × (3√15+3√3)/(3√15+3√3)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = ((9×15)+9√(15×3)+3√(3×15)+(3×3))/((9×15)-(9×3))</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = (135+9√45+3√45+9)/(135-27)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = (144+12√45)/(108)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = (144+12√(9×5))/108</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = (144+36√(5))/108</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = (4+√5)/3</p><p>&nbsp;</p><p><strong>J<u>adi, jawaban yang benar adalah (4+√5)/3.</u></strong></p>