Question

When the square of a bigger 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 of two numbers.

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

Answer: (A)

$1$

Let the larger number be $x$ and the smaller number be $y$
$x^2+y^3=593$ ...(1)
$y^2-x=55$ ...(2)
From the second equation, $x=y^2-55$
Substituting this in the first equation,
$y^4-110y^2+3025+y^3=593$
$y^4+y^3-110y^2+2432=0$
Through hit and trial, we find that $y=8$ satisfies the above equation ($8^4+8^3-110\times 8^2+2432=4096+512-7040+2432=0$ )
Thus, $y=8$ and $x=8^2-55=9$

Thus, the difference between $x$ and $y$ is $1$