Question

(4+ root 5 / 4- root 5) + (4- root 5 / 4+ root 5)

Answer 1

Step-by-step explanation:

(4 +√5)/(4 -√5)  + (4 -√5)/(4 +√5)

now dividing and multiplying the first term by (4 +√5) and second term by (4 -√5), we get,

(4 +√5)×(4 +√5)/(4 -√5)×(4 +√5) + (4 -√5)×(4 -√5)/(4 +√5)×(4 -√5)

⇒(4 +√5)²/(16 -5) +  (4 -√5)²/(16 -5)   ( applying (a² -b²) = (a+b)(a -b))

⇒(16 +5 +8√5 +16 +5 - 8√5)/11

⇒42/11

HOPE IT HELPS.........!

Answer 2

Step-by-step explanation:

$\frac{4 + \sqrt{5} }{4 - \sqrt{5} } + \frac{4 - \sqrt{5} }{4 + \sqrt{5} }$

$by \: \: cross \: \: multiplication$

$\frac{ {(4 + \sqrt{5}) }^{2} }{ {(4 - \sqrt{5}) }^{2} }$

$\frac{16 + 5 + 8 \sqrt{5} }{16 + 5 - 8 \sqrt{5} }$

$\frac{21 + 8 \sqrt{5} }{21 - 8 \sqrt{5} }$

$rationalising \: \: the \: \: denominator$

$\frac{21 + 8 \sqrt{5} }{21 - 8 \sqrt{5} } \times \frac{21 + 8 \sqrt{5} }{21 + 8 \sqrt{5} }$