Question

if a+1/a=2 then find a2+1/a2 expansion chapter
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Answer 1

Question :

If a+1/a = 2 then find a² + 1/a²

Answer :

$\boxed{\bf a^2+\frac{1}{a^2}=2}$

Given :

$a+\frac{1}{a} =2$

To find :

$a^{2} +\frac{1}{a^2} = \ ?$

Solution :

  $a+\frac{1}{a}=2 \\\\ \text{Squaring on both sides,} \\\\ (a+\frac{1}{a})^2=2^2 \\\\ a^2+2(a)(\frac{1}{a})+(\frac{1}{a})^2=4\\\\ a^2+2+\frac{1}{a^2}=4 \\\\ a^2+\frac{1}{a^2}=4-2\\\\ a^2+\frac{1}{a^2}=2$

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>> IDENTITY USED :

$(a+b)^2=a^2+2ab+b^2$

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>> OTHER IDENTITIES :

 $(a-b)^2=a^2-2ab+b^2\\\\ a^2-b^2=(a+b)(a-b) \\\\ (a+b)^3=a^3+3a^2b+3ab^2+b^3\\\\ (a-b)^3=a^3-3a^2b+3ab^2-b^3$

Answer 2

Refer the attachment...........!!!!!!!