Question

HI FRNDS PLZZ help..
with step by step explanation ​

Answer 1

Answer:

Option(3)

Step-by-step explanation:

$Given: \frac{22}{2+\sqrt{3}+\sqrt{5}}$

$\Rightarrow \frac{22}{2+\sqrt{3}+\sqrt{5}} * \frac{2+\sqrt{3}-\sqrt{5}}{2+\sqrt{3}-\sqrt{5} }$

$\Rightarrow \frac{22(2+\sqrt{3}-\sqrt{5})}{(2+\sqrt{3})^2-(\sqrt{5})^2}$

$\Rightarrow \frac{44+22\sqrt{3} -22\sqrt{5} }{2+4\sqrt{3} }$

$\Rightarrow \frac{2(22+11\sqrt{3}-11\sqrt{5})}{2(1+2\sqrt{3}) }$

$\Rightarrow \frac{22+11\sqrt{3}-11\sqrt{5}}{1+2\sqrt{3}}$

$\Rightarrow \frac{22+11\sqrt{3}-11\sqrt{5}}{1+2\sqrt{3}}*\frac{1-2\sqrt{3}}{1-2\sqrt{3}}$

$\Rightarrow \frac{(22+11\sqrt{3}-11\sqrt{5})(1-2\sqrt{3})}{(1)-(2\sqrt{3})^2 }$

$\Rightarrow \frac{(22\sqrt{15} -44-33\sqrt{3} -11\sqrt{5})}{-11}$

$\Rightarrow \boxed{3\sqrt{3}+\sqrt{5} -2\sqrt{15}+4}$

Hope it helps!

Answer 2

22/2+(√3+√5)*2-(√3+√5)/2-(√3+√5)

=22[2-(√3+√5)]/2^2-(√3+√5)^2

=44-22√3+22√5÷4-[√3^2+2*√3*√5+√5^2]

=44-22√15/4(3+2√15+5)

=44-22√15/32+8√15

2(22-11√15)/2(16+4√15)

22-11√15/16+4√15