Question

factorize using algebraic identities: x^2+1/x^2+2​

Answer 1

Answer:

( x + 1/x )^2

Step-by-step explanation:

x^2 +1/2^2 + 2 = ( x^2 )+ ( 1/x^2 )+( 2×x×1/x) = ( x+1/x )^2 . {a^2+b^2+2ab} = { a+b }^2

Answer 2

Answer:

$\underline{\bigstar\:\textsf{According to the Question Now :}}\\\\\implies\tt x + \dfrac{1}{x} = 4 \\\\ \textsf{Squaring Both Sides :} \\\\\implies\tt\bigg(x + \dfrac{1}{x} \bigg)^{2} ={(4)}^{2}\\\\\implies\tt {x}^{2} +\dfrac{1}{{x}^{2}} + 2 \times x \times \dfrac{1}{x} = 16 \\\\\\\implies\tt {x}^{2} +\dfrac{1}{{x}^{2}} = 16 - 2 \\\\\\\implies\tt {x}^{2} +\dfrac{1}{{x}^{2}} =14\\\\ \textsf{Squaring Both Sides :} \\\\\implies\tt \bigg({x}^{2} +\dfrac{1}{{x}^{2}}\bigg) ={(14)}^{2}\\\\\\\implies\tt {x}^{4} +\dfrac{1}{{x}^{4}} + 2 \times{x}^{2} \times\dfrac{1}{{x}^{2}} = 196\\\\\\\implies\tt {x}^{4} +\dfrac{1}{{x}^{4}} = 196 - 2\\\\\\\implies\large\boxed{\tt{x}^{4} +\dfrac{1}{{x}^{4}} = 194}$