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12 Sep 2025, 00:17
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Difficulty:
95%
(hard)
Question Stats:
21% (02:21) correct
79%
(02:22)
wrong
based on 96
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Date
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Find the number of distinct positive integral solutions of \((x^2−9x+19)^{(x^2−17x+72)}=1\)?
A. 6
B. 5
C. 2
D. 3
E. 4
Screenshot 2025-09-12 12.46.17 PM.png [ 37.72 KiB | Viewed 857 times ]
A. 6
B. 5
C. 2
D. 3
E. 4
Attachment:
Screenshot 2025-09-12 12.46.17 PM.png [ 37.72 KiB | Viewed 857 times ]
12 Sep 2025, 03:55
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My logic says this:
it's either x^0 or 1^x
considering x^0:
x^2-17x+172=0 --> (x-9)(x-8)=0 --> 2 solutions
considering 1^x:
x^2-9x+19=1 --> x^2-9x+18=0 --> (x-6)(x-3)=0 --> 2 solutions
IMO E. what am I missing?
it's either x^0 or 1^x
considering x^0:
x^2-17x+172=0 --> (x-9)(x-8)=0 --> 2 solutions
considering 1^x:
x^2-9x+19=1 --> x^2-9x+18=0 --> (x-6)(x-3)=0 --> 2 solutions
IMO E. what am I missing?
