Question

Find the values of p and q, if √5+√3 / √5−√3 - √5−√3 / √5+√3 = + √15 q

Answer 1

Answer:

p = 0, q = 2

Step-by-step explanation:

$Given:\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}-\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}$

$=\frac{(\sqrt{5}+\sqrt{3})^2-(\sqrt{5}-\sqrt{3})^2}{(\sqrt{5}+\sqrt{3})(\sqrt{5}-\sqrt{3})}$

$=\frac{8+2\sqrt{15}-(8-2\sqrt{15})}{(\sqrt{5})^2-(\sqrt{3})^2}$

$=\frac{8+2\sqrt{15}-8+2\sqrt{15}}{5-3}$

$=\frac{4\sqrt{15}}{2}$

$=2\sqrt{15}$

It can be written as,

0 + 2√15

On comparing with p + √15q, we get

0 + 2√15 = p + √15q

p = 0, q = 2

Hope it helps!

Answer 2

Answer:

$\pink{\boxed{\mathfrak{p=0}}}\\\\\ted{\boxed{\mathfrak{q=2}}}$

Step-by-step explanation:

L.H.S

$\mathsf{\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}-\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}}$

$\implies\mathsf{\frac{(\sqrt{5}+\sqrt{3})^2-(\sqrt{5}-\sqrt{3})^2}{(\sqrt{5}+\sqrt{3})(\sqrt{5}-\sqrt{3})}}$

$\implies\mathsf{\frac{5+3+2\sqrt{15}-(5+3-2\sqrt{15})}{(\sqrt{5})^2-(\sqrt{3})^2}}$

$\implies\mathsf{\frac{8+2\sqrt{15}-(8-2\sqrt{15})}{(\sqrt{5})^2-(\sqrt{3})^2}}$

$\implies\mathsf{\frac{8+2\sqrt{15}-8+2\sqrt{15}}{5-3}}$

$\mathsf{\implies \frac{4\sqrt{15}}{2}}$

$\mathsf{\implies 2\sqrt{15}}$

L.H.S = R.H.S

$\mathsf{2\sqrt{15}=p+\sqrt{15}q}$

$\mathsf{0+2\sqrt{15}=p+\sqrt{15}q}$

$\underline{\textsf{From this compare the rational and irrational values :}}$

$\mathsf{p=0}$

$\mathsf{q\sqrt{15}=2\sqrt{15}}$

$\mathsf{q=2}$