Question

if x=√15+√3 and y=√10+√8 what is the relation between xand y​

Answer 1

To find: The relation between $x$ and $y$

Solution:

Given,

$\quad\quad\quad x=\sqrt{15}+\sqrt{3}$

$\quad\quad\quad y=\sqrt{10}+\sqrt{8}$

We can find a relation between $x$ and $y$ using many operations of algebra.

1. We add the terms:

$\quad x+y=\sqrt{15}+\sqrt{3}+\sqrt{10}+\sqrt{8}$

$\Rightarrow \color{blue}{x+y=\sqrt{15}+\sqrt{10}+\sqrt{8}+\sqrt{3}}$

This can be a relation between $x$ and $y$.

2. We subtract the terms:

$\quad x-y=\sqrt{15}+\sqrt{3}-\sqrt{10}-\sqrt{8}$

$\Rightarrow \color{blue}{x-y=\sqrt{15}-\sqrt{10}-\sqrt{8}+\sqrt{3}}$

This can be a relation between $x$ and $y$.

3. We multiply the terms:

$\quad xy=(\sqrt{15}+\sqrt{3})(\sqrt{10}\sqrt{8})$

$\Rightarrow \color{blue}{xy=\sqrt{150}+\sqrt{120}+\sqrt{30}+\sqrt{24}}$

This can be a relation between $x$ and $y$.