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The sum of squares two numbers is $26$ and difference is $8$. Find the numbers.
Given: The sum of squares two numbers is $26$ and difference is $8$.
To do: To find the numbers.
Solution:
Let $x$ and $y$ be the numbers.
According to the question:
$x^2+y^2=26$ ........ $( i)$
$x^2-y^2=8$ .......... $( ii)$
Add both $( i)$ and $( ii)$
$\Rightarrow x^2+y^2+x^2-y^2=26+8$
$\Rightarrow 2x^2=34$
$\Rightarrow x^2=17$
$\Rightarrow x=\sqrt{17}$
Place the value of $x$ in the equation $x^2-y^2=8$
$\Rightarrow 17-y^2=8$
$\Rightarrow y^2=17-8$
$\Rightarrow y^2=9$
$\Rightarrow y=3$
The value of the given numbers are
$x=\sqrt{17}$ and $y=3$.
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