Question

x= √5+2 then x^2+1/x^2=

Answer 1

Answer:

ans=10+4√5/8+4√5

Step-by-step explanation:

(x^2+1)/X^2

{(2+√5)^2+1}/(2+√5)^2

(4+4√5+5+1)/4+4√5+5

(10+4√5)/9+4√5

Answer 2

$\sf\huge\ your \:answer=18\\\\\bf\ \: here \: x = \sqrt{5} + 2 \\ \\ \therefore \sf\ {x}^{2} = {( \sqrt{5} + 2)}^{2} \\ \\ \sf\ \implies: {x}^{2} = {( \sqrt{5} )}^{2} + 2 \times \sqrt{5} \times 2 + {(2)}^{2} \\ \\ \sf\ \implies: {x}^{2} = 5 + 4 \sqrt{5} + 4 \\ \\ \sf\boxed{ \bf\ \implies: {x}^{2} = 9 + 4 \sqrt{5} } \\ \\ \tt\boxed{ \because \frac{1}{ {x}^{2} } = \frac{1}{9 + 4 \sqrt{5} } } \\ \\ \bf\ \: now \: \: ({x}^{2} + \frac{1}{ {x}^{2} }) \\ \\ \sf\ \implies: (9 + 4 \sqrt{5} ) + ( \frac{1}{9 + 4 \sqrt{5} } ) \\ \\ \sf\ \implies: \frac{ {(9 + 4 \sqrt{5} )}^{2} + 1}{9 + 4 \sqrt{5} } \\ \\\sf\ \implies: \frac{ {( 9)}^{2} + 2 \times 9 \times 4 \sqrt{5} + {(4 \sqrt{5} )}^{2} + 1 }{9 + 4 \sqrt{5} } \\ \\ \sf\ \implies: \frac{81 + 81 + 72 \sqrt{5} }{9 + 4 \sqrt{5} } \\ \\ \sf\ \implies: \frac{162 + 72 \sqrt{5} }{9 + 4 \sqrt{5} } \\ \\ \sf\ \implies: \frac{18( \cancel{9 + 4 \sqrt{5} )}}{ \cancel{9 + 4 \sqrt{5}} } \\ \\\sf\boxed{ \implies:18 }$