Question

If the difference of two number is $8$ and the difference of their square is $160$. What are the numbers?

Answer 1

Find the unknown numbers.
Let $x$ and $y$ are two unknown numbers.

Given: The difference of two number is $8$

$\Rightarrow$ $x-y=8$ …………$\left[1\right]$

Given: The difference of their squares is $160$.

$\Rightarrow$ $x^2-y^2=160$

Substitute value of $x$ from equation $1$

$\Rightarrow$ ${(8+y)}^2-y^2=160$

$\Rightarrow$$64+y^2+16y-y^2=160$

$\Rightarrow$ $16y=96$

$\Rightarrow$ $y=\frac{96}{16}$

$\Rightarrow$ $y=6$

From equation $1$:

$x=8+y$

$\Rightarrow$ $x=8+6$

$\Rightarrow$ $x=14$

Hence, the two unknown numbers are $6$ and $14$.