Quant Question Of The Day: 102
Algebra.
Find the number of integer solutions of the equation x² + 12 = y⁴.
Find the number of integer solutions of the equation x² + 12 = y⁴.
x²+ 12 = y⁴
y⁴ – x2= 12
(y² + x)(y²- x) = 12 = 1•12 = 2•6 = 3•4
No solutions for 1•12 and 3•4 factor pairs as RHS(=12) is even hence we need just even•even factor pairs.
(y² + x)(y² – x) = 2•6
y=±2nd x=±2
4 solutions.
1
2 i.e. (2,2) and (-2,-2)