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 $y=3$.

Updated on: 10-Oct-2022

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