Question

2/(sqrt(5) + sqrt(3)) + 1/(sqrt(3) + sqrt(2)) - 3/(sqrt(5) + sqrt(2))​

Answer 1

Answer:

0

Step-by-step explanation:

2/$\sqrt{5}$+$\sqrt{3}$  + 1/

    ↓                  ↓               ↓

    x                   y               z  (let)

$x+y-z-----(1)$

$x=2/\sqrt{5} +\sqrt{3}$

$x=$$2/\sqrt{5} +\sqrt{3} * \sqrt{5} -\sqrt{3} / \sqrt{5} -\sqrt{3}$

[$a^{2} +b^{2} =(a+b)(a-b)$]

$x=$$(\sqrt{5} -\sqrt{3} ) / 2$

$x=\sqrt{5} -\sqrt{3}$

Now,

$y=1/\sqrt{3} +\sqrt{2}$

$y=1/\sqrt{3} +\sqrt{2} * \sqrt{3} -\sqrt{2} /\sqrt{3} -\sqrt{2} \\y=\sqrt{3} -\sqrt{2}$

And,

$z=3/\sqrt{5} +\sqrt{2} \\z=3/\sqrt{5} +\sqrt{2} * \sqrt{5} -\sqrt{2} /\sqrt{5} -\sqrt{2} \\z=\sqrt{5} -\sqrt{2}$

Put the values of x,y and z in equation (1)

$x+y-z=\sqrt{5} -\sqrt{3} +\sqrt{3} -\sqrt{2} -\sqrt{5} +\sqrt{2} \\x+y-z=0 Ans.$