The number of integer solutions of the equation (x²-10)(x²-3x-10)=1 is
Question:
The number of integer solutions of the equation (x²-10)(x²-3x-10)=1 is
The number of integer solutions of the equation (x²-10)(x²-3x-10)=1 is
Options
Answer: (3) 4
Explanation:
For product to equal 1, both factors must be 1 or both -1. Case 1: x²-10=1 and x²-3x-10=1 gives x²=11 and x²-3x-11=0. Case 2: x²-10=-1 and x²-3x-10=-1 gives x²=9 and x²-3x-9=0, yielding x=±3 and checking x=3 works. Total 4 integer solutions.
Explanation:
For product to equal 1, both factors must be 1 or both -1. Case 1: x²-10=1 and x²-3x-10=1 gives x²=11 and x²-3x-11=0. Case 2: x²-10=-1 and x²-3x-10=-1 gives x²=9 and x²-3x-9=0, yielding x=±3 and checking x=3 works. Total 4 integer solutions.
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