Question

Find x^2 from x= √5-2/√5+2

Answer 1

x = (√5-2)/(√5+2)

After rationalization,

x = (√5-2)²/[(√5)² -2²]

x = (5+4-4√5)/(5-4)

x = (9-4√5)/1

x = 9-4√5

Square on both sides,

x² = (9-4√5)²

x² = 81 +80-72√5

x² =161-72√5

I hope this will help you

-by ABHAY

Answer 2

Heya !!!!

♦ Given ♦

$x = \frac{ \sqrt{5} - 2}{ \sqrt{5} + 2 }$

Rationalising the denominator
$\frac{ \sqrt{5} - 2}{ \sqrt{5 } + 2 } \times \frac{ \sqrt{5} - 2}{ \sqrt{5} - 2 } \\ \\ = \frac{ (\sqrt{5} - 2) {}^{2} }{5 - 4} \\ \\ = 5 - 4 \sqrt{5} + 4 = 9 - 4 \sqrt{5}$

x² = ( 9 - 4√5 ) ²

x² = 81 - 72√5 + 80

x² = 161 - 72√5

x² = 161 - 72 × ( 2.23... )

x² = 161 - 160.56

x² = 0.44