Question

The statement “the sum of the squares of \[x\] and \[y\] is equal to the square root of the difference of \[x\] and \[y\]” can be mathematically represented as:
A.\[{x^2} + {y^2} = \sqrt {x - y} \]
B.\[{x^2} - {y^2} = \sqrt {x + y} \]
C.\[{\left( {x + y} \right)^2} = \sqrt x - \sqrt y \]
D.\[\sqrt {x + y} = {\left( {x - y} \right)^2}\]

Answer 1

Hint: Here, we will take the squares of \[x\] and \[y\] and then add them. Then we will take the obtained sum as equal to the square root of the difference of \[x\] and \[y\].

Complete step-by-step answer:
First, we will find the square of \[x\].
\[ \Rightarrow {x^2}{\text{ .......eq.(1)}}\]
Then we will find the square of \[y\].
\[ \Rightarrow {y^2}{\text{ .......eq.(2)}}\]
Adding the equation (1) and equation (2), we get
\[ \Rightarrow {x^2} + {y^2}{\text{ ......eq.(3)}}\]
Subtracting \[y\] from \[x\], we get
\[ \Rightarrow x - y\]
Taking the square root in the above equation, we get
\[ \Rightarrow \sqrt {x - y} {\text{ .....eq.(4)}}\]
Taking equation (3) equal to equation (4) as given in the problem, we get
\[ \Rightarrow {x^2} + {y^2} = \sqrt {x - y} \]
Hence, option A is correct.

Note: We need to know that the mathematical representation of a statement is a very general relationship that expresses similarities (or equivalences) between mathematical objects or structures. This problem is simple, we just have to follow each step by step properly. Avoid calculation mistakes.