Question

When the square of a number and the cube of a small number are added the result is $593$. If the square of the smaller number exceeds the bigger number by $55$. Find the difference between two numbers.

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is A $1$

Solution:-

Let the two numbers be $x$ and $y$ such that $x>y$.

$x^2+y^3=593$

$y^2=x+55$

From the second equation we know that $y+55$ is a perfect square. Therefore $x=9$ and $y=8$ is one possible combination.

$x=8$ and $y=9$ fit the bill for the first equation too because $8^3+9^2=593$

Therefore $x-y=1$