An algebra problem by Hemanth Sparks

Algebra Level 2

Gautam father bought some apples he asked how many apples his father said if we remove one apple it will be a perfect square if we add one apple it will be a perfect cube find number of apples


The answer is 26.

Hemanth Sparks by Hemanth Sparks , 20, India

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1 solution

The equations are: x − 1 = a 2 x-1=a^2 x + 1 = b 3 x+1=b^3 Subtracting the second equation from the first equation,we get: − 2 = a 2 − b 3 → 2 = b 3 − a 2 → a 2 + 2 = b 3 -2=a^2-b^3\rightarrow 2=b^3-a^2\rightarrow a^2+2=b^3 Now by trial and error method,we get that a 2 = 25 , b 3 = 27 a^2=25,b^3=27 which means that a = 5 , b = 3 a=5,b=3 so x = 26 x=\boxed{26}

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