Question

If m+1/m = 4, show that m²+(1/m)² = 14​

Answer 1

Answer:

(i) m2 + (1/m2) = (m – (1/m))2 + 2. = (5)2 + 2 = 25 + 2 = 27. (ii) m4 + (1/m4) = ( m2 + (1/m2)2 – 2. = (27)2 – 2 = 729 – 2 = 727.

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

$m + \frac{1}{m} = 4 \\ (m + \frac{1}{m} )^{2} = {4}^{2} \\ m^{2} + { \frac{1}{m} }^{2} + 2m \frac{1}{m} = 16 \\ \\ m ^{2} + \frac{1}{m ^{2} } + 2 = 16 \\ m^{2} + \frac{1}{ {m}^{2} } = 16 - 2 \\ m ^{2} + \frac{1}{ {m}^{2} } = 14$

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