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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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\(\large \color{black}{\begin{align} & \normalsize \text{Choose the incorrect relation(s) from the following}\hspace{.33em}\\~\\ & i.)\ \sqrt{6}+\sqrt{2}=\sqrt{5}+\sqrt{3}\hspace{.33em}\\~\\ & ii.)\ \sqrt{6}+\sqrt{2}<\sqrt{5}+\sqrt{3}\hspace{.33em}\\~\\ & iii.)\ \sqrt{6}+\sqrt{2}>\sqrt{5}+\sqrt{3}\hspace{.33em}\\~\\ & a.)\ i.) \ \text{and}\ iii.)\hspace{.33em}\\~\\ & b.)\ ii.) \ \text{and}\ iii.)\hspace{.33em}\\~\\ & c.)\ i.) \hspace{.33em}\\~\\ & d.)\ ii.) \hspace{.33em}\\~\\ \end{align}}\)
i have to solve this with in a minute
If a calculator is allowed you could just calculate the decimal values of both sides and check if they are equal.

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lol no calculator is allowed
In view of arriving at a contradiction, lets suppose that \(\sqrt{6}+\sqrt{2}=\sqrt{5}+\sqrt{3}\). Square both sides and get \(6+2+2\sqrt{12}=5+3+2\sqrt{15}\). \(\implies \sqrt{12}=\sqrt{15}\) which is wrong. So the initial assumption is wrong.
ok
Alternatively you may work it like this : \[\large{\begin{align} \sqrt{6}+\sqrt{2}~~&\stackrel{?}{}~~\sqrt{5}+\sqrt{3}\\~\\ (\sqrt{6}+\sqrt{2})^2~~&\stackrel{?}{}~~(\sqrt{5}+\sqrt{3})^2\\~\\ 6+2+2\sqrt{12}~~&\stackrel{?}{}~~ 5+3+2\sqrt{15}\\~\\ \sqrt{12}~~&\stackrel{?}{}~~ \sqrt{15}\\~\\ \sqrt{12}~~&\lt~~ \sqrt{15} \end{align}}\] since the numbers are positive, the implications will work in the reverse direction also. read it from bottom to top.
option 1 is incorrect
i and iii are wrong
thnks

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