Question

If x = √5+2 find the value of x2 + 1/x2

Answer 1

18

Explanation:

If we plug (√5+2) into the equation x^2 + 1/x^2, you will get:

(√5+2)^2 + 1/(√5+2)^2

Then just plug it into a calculator and you're golden.

Answer 2

`\huge\fbox{Answer ☘}`

x = √5 + 2

`x {}^(2) + \frac{1}{ x {}^(2) } = ?\\ \\( √(5) + 2) {}^(2) + \frac{1}{( √(5) + 2) {}^(2) } \\\\ = > (5 + 4 √(5) + 4) + ( (1)/(5 + 4 √(5) + 4)) \\\\ = > (4 √(5) + 9) + ( (1)/(4 √(5) + 9 ) ) \\ \\ = > \frac{(4 √(5 ) + 9) {}^(2) +1 }{4 √(5) + 9} \\\\ = > (80 + 81 + 72 √(5) + 1)/(4 √(5) + 9) \\\\ = > (162 + 72 √(5) )/(4 √(5) + 9) \\ \\= > (16 + 72 √(5) )/(4 √(5) + 9) * (4 √(5) - 9)/(4 √(5) - 9) \\\\ = > (64 √(5 ) - 144 + 1440 - 648 √(5) )/(80 - 81) \\ \\ = > (1296 - 584 √(5) )/( - 1) \\\\\bold\pink{ = > 584 √(5) - 1296}`

hope helpful~