Latest CAT Aptitude Question SOLUTION: Find solutions of A^2 = B^3 − 432.GIVEN THAT A and B are integers.

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Find solutions of
A^2 = B^3 − 432.GIVEN THAT A and B are integers.

Asked In CAT jyotish r (11 years ago)

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jyotish r  (11 years ago)

SORRY , SOME TYPING ERROR!!!
− MEANS -

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Vignesh  (11 years ago)

A = 36 ; B = 12

A^2 = B^3 - 432
36^2 = 12^3 - 432
1296 = 1728 - 432
1296 = 1296
Proved.

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Soni  (11 years ago)

A = 36

B = 12

A^2 = B^3 - 432

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Garima  (11 years ago)

a=3 and
b=4

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Shiv Kumar  (11 years ago)

question has typo errors. Hence it is closed

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jyotish r  (11 years ago)

A=+36 OR -36
B=12
B^3 = A^2 + 432 is a perfect cube IMPLIES THAT 6^3(A^2 + 432) = 216(A^2 + 432) is a perfect cube.
But 216(A^2 + 432) = (A + 36)^3 − (A − 36)^3.


Hence (6B)^3 + (A− 36)^3 = (A + 36)^3.

a^n + b^n = c^n has no non-zero integer solutions for a, b and c, when n > 2
So here solution exists when A=+36 OR -36
In this case 6B=72
B=12

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