Question

If p = (√5-√3)/(√5+√3)
and q=
(√5 + √3)/(√5-√3)
find the value of p^2 + q^2​

Answer 1

Answer:

371243

Step-by-step explanation:

first

Answer 2

Step-by-step explanation:

$p = \frac{ \sqrt{5} - \sqrt{3} }{ \sqrt{5 } + \sqrt{3} }$

$p = \frac{ \sqrt{5 } - \sqrt{3} }{ \sqrt{5} + \sqrt{3} } \times \frac{ \sqrt{5} - \sqrt{3} }{ \sqrt{5} - \sqrt{3} }$

$p = \frac{8 - 2 \sqrt{15} }{2}$

$p = 4 - \sqrt{15}$

$q = \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} }$

$q = \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} } \times \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} + \sqrt{3} }$

$q = \frac{8 + 2 \sqrt{15} }{2}$

$q = 4 + \sqrt{15}$

${p}^{2} + {q}^{2} = (4 - \sqrt{15})² + (4 + \sqrt{15})²$

$= 16 +15 - 8\sqrt{15} + 15 + 16 + 8\sqrt{15}$

$= 31 + 31$

= 62