Question

Pls solve the above question
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Answer 1

Explanation:

Given expressions are,

`p=(√(10)-√(5))/(√(10)+√(5))` and
`q=(√(10)+√(5))/(√(10)-√(5))`

Remove the radicals from the denominator from both the expressions.

`p=(√(10)-√(5))/(√(10)+√(5)) * (√(10)-√(5))/(√(10)-√(5))`

`=((√(10)-√(5))^2)/((√(10))^2-(√(5))^2)`

`=((√(10)-√(5))^2)/(5)`

`√(p)=\sqrt{((√(10)-√(5))^2)/(5)}`

`=(√(10)-√(5))/(√(5))`

`q=(√(10)+√(5))/(√(10)-√(5))`

`=(√(10)+√(5))/(√(10)-√(5))* (√(10)+√(5))/(√(10)+√(5))`

`=((√(10)+√(5))^2)/((√(10))^2-(√(5))^2)`

`=((√(10)+√(5))^2)/(5)`

`√(q)=\sqrt{((√(10)+√(5))^2)/(5)}`

`=((√(10)+√(5)))/(√(5))`

`√(q)-√(p)-2√(pq)=((√(10)+√(5)))/(√(5))-((√(10)-√(5)))/(√(5))-2(((√(10)+√(5)))/(√(5)))(((√(10)-√(5)))/(√(5)))`

`=(1)/(√(5))(√(10)+√(5)-√(10)+√(5))-(2)/(5)[(√(10))^2-(√(5))^2)]`

`=(1)/(√(5))(2√(5))-(2)/(5)(10-5)`

`=2-2`

`=0`