Question

if x-1/x=√5, find the values of
i) x + 1/x
ii) x^3+1/x^3
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Answer 1

Answer:

Step-by-step explanation:

Answer 2

$HEYA \: \\ \\ x - (1 \div x) = \sqrt{5} \: \: (given) \\ \\ 1) \: \: x + (1 \div x) = \\ \sqrt{(x - (1 \div x)) {}^{2} + 4} \\ \\ (x + (1 \div x)) = \\ \sqrt{(5 + 4)} \\ \\ (x + (1 \div x)) = ±3 \\ \\ 2) \\ (x - (1 \div x) = \sqrt{5} \\ cubing \: on \: both \: sides \: we \: have \: \\ \\ (x - (1 \div x)) {}^{3} = 5 \sqrt{5} \\ \\ x {}^{3} + (1 \div x {}^{3} ) - 3(x - (1 \div x)) = 5 \sqrt{5} \\ \\ x {}^{3} + (1 \div x {}^{3} ) = 5 \sqrt{5} +3 \sqrt{5} \\ \\ x {}^{3} + (1 \div x {}^{3} ) = 8 \sqrt{5}$