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
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B
2
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C
3
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D
4
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Solution
The correct option is B1 Let the larger number be x and the smaller number be y x2+y3=593 ...(1) y2−x=55 ...(2) From the second equation, x=y2−55 Substituting this in the first equation, y4−110y2+3025+y3=593 y4+y3−110y2+2432=0 Through hit and trial, we find that y=8 satisfies the above equation (84+83−110×82+2432=4096+512−7040+2432=0 ) Thus, y=8 and x=82−55=9 Thus, the difference between x and y is 1