Question

if a+1/a=2, find the value of: i) a2+1/a2 ii) a4+1/a4​

Answer 1

Step-by-step explanation:

$a + \frac{1}{a} = 2 \\ \\ \frac{ {a}^{2} + 1}{a} = 2 \\ \\ {a }^{2} - 2a + 1 = 0 \\ \\ {a}^{2} - a - a + 1 \\ \\ a(a - 1) - 1(a - 1) \\ \\ (a - 1)(a - 1) \\ \\ a = 1 \\ \\ \\ \\ now \\ \\ 1) {a}^{2} + \frac{1}{ {a}^{2} } \\ \\ {(1)}^{2} + \frac{1}{(1) {}^{2} } \\ \\ 1 + 1 \\ \\ = 2 \\ \\ \\ \\ 2) {a}^{4} + \frac{1}{ {a}^{4} } \\ \\ {(1)}^{4} + \frac{1}{ {(1)}^{4} } \\ \\ 1 + 1 \\ \\ = 2$

Answer 2

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