Question

Prove that
$\frac{1}{ \sqrt{2} + \sqrt{3} - \sqrt{5} } + \frac{1}{ \sqrt{2} - \sqrt{3} - \sqrt{5} } = \frac{1}{ \sqrt{2} } = \frac{ \sqrt{2} }{2}$
Salmonpanna2022 please solve this question.

Wrong answer will be reported.​

Answer 1

Step-by-step explanation:

Question:

Prove that:

$\frac{1}{ \sqrt{2} + \sqrt{3} - \sqrt{5} } + \frac{1}{ \sqrt{2} - \sqrt{3} - \sqrt{5} } = \frac{1}{ \sqrt{2} } = \frac{ \sqrt{2} }{2}$

Solution:

$\frac{1}{ \sqrt{2} + \sqrt{3} - \sqrt{5} } + \frac{1}{ \sqrt{2} - \sqrt{3} - \sqrt{5} } = \frac{1}{ \sqrt{2} } = \frac{ \sqrt{2} }{2} \\ = > \frac{1}{ \sqrt{2} - \sqrt{3} - \sqrt{5} } = \frac{ \sqrt{2} + \sqrt{3} + \sqrt{5} }{( \sqrt{2} + \sqrt{3} )^{2} - ( { \sqrt{5}) }^{2} } \\ = \frac{ \sqrt{2} + \sqrt{3} + \sqrt{5} }{2 + 3 + 2 \times \sqrt{2} \times \sqrt{3} - 5} = \frac{ \sqrt{2} + \sqrt{3} + \sqrt{5} }{5 + 2 \sqrt{6} - 5 } = \frac{ \sqrt{2} + \sqrt{3} + \sqrt{5} }{2 \sqrt{6} }$

Again,

$\frac{1}{ \sqrt{2} - \sqrt{3} - \sqrt{5} } = \frac{ \sqrt{2} - \sqrt{3} + \sqrt{5} }{( \sqrt{2} - \sqrt{3} )^{2} - ( { \sqrt{5}) }^{2} } \\ = \frac{ \sqrt{2} - \sqrt{3} + \sqrt{5} }{2 + 3 - 2 \sqrt{6} - 5 } = \frac{ \sqrt{2} - \sqrt{3} + \sqrt{5} }{ - 2 \sqrt{6} }$

Now LHS=

$\frac{1}{ \sqrt{2} + \sqrt{3} - \sqrt{5} } + \frac{1}{ \sqrt{2} - \sqrt{3} - \sqrt{5} } = \frac{ \sqrt{2} + \sqrt{3} + \sqrt{5} }{2 \sqrt{6} } + \frac{2 \sqrt{5 } - \sqrt{3} + \sqrt{5} }{ - 2 \sqrt{6} } \\ = \frac{ \sqrt{2} + \sqrt{3} + \sqrt{5} }{2 \sqrt{6} } - \frac{ \sqrt{2} - \sqrt{3} \sqrt{5} }{2 \sqrt{6} } \\ = \frac{ \sqrt{2} + \sqrt{3} + \sqrt{5} - \sqrt{2} - \sqrt{3} - \sqrt{5} }{2 \sqrt{6} } \\ = \frac{2 \sqrt{3} }{2 \sqrt{6} } = \sqrt{ \frac{3}{6} } = \frac{1}{ \sqrt{2} } = \frac{ \sqrt{2} }{2} \: rhs.$

Answer 2

Answer:

hence it is proved that LHS = RHS

Total Population=700

Sample Chosen =120

Respondent who like student Peas =34

Respondent who like green beans 27

Respondent who like broccoli =23

Respondent who like zucchini=18

Respondent who like brussels sprouts= 18

Out of 120, 23 likes Broccoli, which can be represented in terms of fraction as

23 120

So, if out of 700, who likes broccoli, is x, which can be calcı ted as

hope it helps have a great day

thanks