If x is a positive real number such that x8 + 1x8 = 47, then the value of x9 + 1x9 is
Explanation:
Given, x8 + 1x8 = 47
⇒ x8 + 1x8 + 2 = 49
⇒ (x4)2 + 1x42 + 2×x4×1x4 = 49
⇒ x4+1x42 = 49
⇒ x4+1x4 = 7 [-7 will be rejected as LHS should be positive]
Now, x4+1x4 + 2 = 9
⇒ x22+1x22 + 2×x2×1x2 = 9
⇒ x2+1x22 = 9
⇒ x2+1x2 = 3
Similarly, x+1x = 5
Cubing both sides, we get
⇒ x3 + 1x3 + 3×x×1xx+1x = 5√5
⇒ x3 + 1x3 = 2√5
Again cubing both sides, we get
⇒ x9 + 1x9 + 3×x3×1x3x3+1x3 = 40√5
⇒ x9 + 1x9 = 34√5
Hence, option (a).
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