
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
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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.
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.
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