aakgoel wrote:If,
a+b+c=1
a^2+b^2+c^2=35
a^3+b^3+c^3=97
Find,
a^4+b^4+c^4
a^5+b^5+c^5
a²+b²+c² = 35.
Perfect squares less than 35: 1,4,9,16,25.
The following combination works: 1+9+25 = 35.
Thus, we have the following options for a, b and c: ±1, ±3, and ±5.
The following combination will yield a sum of 1:
a+b+c = -1 + (-3) + 5 = 1.
If a=-1, b=-3, and c=5, then a³+b³+c³ = (-1) + (-27) + 125 = 97.
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