1/4 - √ 8 + 3 + 2√2/3 - 2√2 – 3 - 2√2/3 + 2√2 = a + b√2 Rationalizing each we get 1/4 - √8 → 1/4 -√8 × 4 + √8 / 4 + √8 = 4 + √8 / 8 Same for other values = 3 + 2√2 / 3 – 2√2 = 17 + 12√2 = 3 - 2√2 / 3 + 2√2 = 17 - 12√2 = 4 + √8 / / + 17 + 12√2 – 17 + 12√2 On solving 1/2 + 97√2/4 = a + b√2 So, a = 1/2 and b = 97/4 (3 × 1/2 + 4 × 97/4) = 3/2 + 97 = 197/2
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