Question

a+1/a= 2 find a²+1/a² and a⁴+1/a⁴​

Answer 1

Step-by-step explanation:

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Answer 2

Given:-

• $\sf{a + \dfrac{1}{a} = 2}$

To find:-

• $\sf{a^2 + \dfrac{1}{a^2} = ?}$

• $\sf{a^4 \dfrac{1}{a^4} = ?}$

Solution:-

• $\sf{a + \dfrac{1}{a} = 2}$

$\implies$ Squaring both side:-

• $\sf{ \bigg(a + \dfrac{1}{a} \bigg)^2 = (2)^2}$

• $\sf{a^2 + \bigg( \dfrac{1}{a} \bigg)^2 + 2 \times \cancel{a} \times \dfrac{1}{ \cancel{a}}= 4}$

• $\sf{a^2 + \dfrac{1}{a^2} = 4 - 2}$

• $\bold{\underline{\boxed{\sf{\pink{\dag \; a^2 + \dfrac{1}{a^2} = 2}}}}}$ --------(1)

★ Now, From equation (1):-

$\implies$ Squaring both side:-

• $\sf{ \bigg( a^2 + \dfrac{1}{a^2} \bigg)^2 = (2)^2}$

• $\sf{a^4 + \bigg( \dfrac{1}{a^2} \bigg)^2 + 2 \times \cancel{a^2} \times \dfrac{1}{ \cancel{a^2}}= 4}$

• $\sf{a^4 + \dfrac{1}{a^4} = 4 - 2}$

• $\bold{\underline{\boxed{\sf{\pink{\dag \; a^4 + \dfrac{1}{a^4} = 2}}}}}$

$\rule{200}{2}$