Question

pls find the ans.....pls help me​

Answer 1

Answer:

$i) \frac{a^{4}+1}{a^{2}} = 2$

$ii) ii) \frac{a^{8}+1}{a^{4}} = 2$

Step-by-step explanation:

$Given \: a + \frac{1}{a} = 2 \: ---(1)$

$i) \frac{a^{4}+1}{a^{2}}\\= \frac{a^{4}}{a^{2}} + \frac{1}{a^{2}}\\= a^{2} + \frac{1}{a^{2}}\\= \left(a+\frac{1}{a}\right)^{2} - 2\\= 2^{2} - 2\\= 4 - 2\\= 2\:--(2)$

$ii) \frac{a^{8}+1}{a^{4}}\\= \frac{a^{8}}{a^{4}} + \frac{1}{a^{4}}\\= a^{4} + \frac{1}{a^{4}}\\= \left(a^{2}+\frac{1}{a^{2}}\right)^{2} - 2\\= 2^{2} - 2\\= 4 - 2\\= 2\:--(3)$

Therefore.,

$i) \frac{a^{4}+1}{a^{2}} = 2$

$ii) ii) \frac{a^{8}+1}{a^{4}} = 2$

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