7^x + 6^x - 2^x = 9^x
List all integer solutions of the above equation.
A graph shows that 7^x+6^x-2^x-9^x approaches zero asymptotically to the left of approximately x=-1, and decreases without limit to the right of x=2, so only x values between -10 and 20 were checked:
>> expo7629
-10 -0.000976542708492336
-9 -0.00195300357121244
-8 -0.0039055043898668
-7 -0.00780792256439464
-6 -0.0155969483461633
-5 -0.031078835246497
-4 -0.0614643177241409
-3 -0.118826660587809
-2 -0.214159737969262
-1 -0.301587301587302
0 0
1 2
2 0
3 -178
4 -2880
5 -34498
6 -367200
7 -3679618
8 -35602560
9 -336989698
10 -3143844000
11 -29040937858
12 -266411471040
13 -2431916132098
14 -22120205234400
15 -200673385632898
16 -1.81696614844032e+15
17 -1.64276245263657e+16
18 -1.48364661742682e+17
19 -1.33884346274813e+18
20 -1.20742170343203e+19
>>
Only 0 and 2 are roots.
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Posted by Charlie
on 2021-09-27 13:13:35 |
listing the possibilities--solution
