Question

If a= √2+1 find value of: i) a+1/a ii) a -1/a​

Answer 1

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GIVEN:-

• $a = \sqrt{2} + 1$

TO FIND:-

(i)

• $a + \frac{1}{a}$
• $( \sqrt{2 } + 1) + \frac{1}{ (\sqrt{2} + 1)}$
• $\sqrt{2} + 1 + \frac{1 \times ( \sqrt{2} - 1) }{( \sqrt{2} + 1)( \sqrt{2} - 1)}$
• $\sqrt{2} + 1 + \frac{ \sqrt{2} - 1 }{2 - 1}$
• $\sqrt{2} + 1 + \sqrt{2} - 1$
• $2 \sqrt{2}$

(ii)

• $a - \frac{1}{a}$
• $( \sqrt{2} + 1) - ( \frac{1}{ \sqrt{2} - 1 } )$
• $\sqrt{2} + 1 - \frac{1}{ \sqrt{2} + 1 }$
• $\sqrt{2} + 1 - \frac{1( \sqrt{2} - 1)}{( \sqrt{2} + 1)( \sqrt{2} - 1)}$
• $\sqrt{2} + 1 - \frac{ \sqrt{2} - 1}{2 - 1}$
• $\sqrt{2} + 1 - ( \sqrt{2} - 1)$
• $\sqrt{2} + 1 - \sqrt{2} + 1$
• $2$