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x = (√5 – √3)/(√5 + √3) y = 1/x ⇒ (√5 + √3)/(√5 – √3) (x + y) = [{(√5 – √3)/(√5 + √3)} + {(√5 + √3)/(√5 – √3)}] ⇒ (x + y) = [(√5 – √3)2 + (√5 + √3)2]/[(√5 – √3)(√5 + √3)] ⇒ (x + y) = [5 + 3 – 2 √15 + 5 + 3 + 2√15]/[(√5)2 – (√3)2] ⇒ (x + y) = 16/(5 – 3) = 16/2 = 8 (x + y)3 = x3 + y3 + 3 × x × y × (x + y) ⇒ x3 + y3 = (x + y)3 - 3 × x × (1/x) × (x + y) ⇒ 83 - 3 × 8 ⇒ 512 – 24 ⇒ 488 ∴ The value of (x3 + y3) is 488.
120, 125, 140, 165, 210, 245
2, 4, 16, 48, 240, 1440, 10080
5, 13, 41, 185, 1111, 8149
Find the wrong number in given number series.
2556, 2613, 2734, 2841, 3012, 3221
-2, 0, 8, 32, 64, 66
171, 86, 87, 132, 266, 668
1, 18, 44, 81, 131, 198
123, 155, 198, 246, 301, 363