perplexus.info :: Numbers : Summing Powers 2

Summing Powers 2 (Posted on 2007-08-25)

What is x + y + z if the following are true:

x⁴ + y⁴ + z⁴ = 11
x³ + y³ + z³ = 7
x² + y² + z² = 3

Just think of this problem as the reverse of this one.

Submitted by Brian Smith

Rating: 4.0000 (4 votes)

Solution: (Hide)

The following identity shows the relationship between the sum and the sums of powers:
6*(x^4+y^4+z^4) = (x+y+z)^4 + 3*(x^2+y^2+z^2)^2 - 6*(x^2+y^2+z^2)(x+y+z)^2 + 8*(x^3+y^3+z^3)(x+y+z)

Let x + y + z = N and substitute:
6*11 = N^4 + 3*3^2 - 6*3*N^2 + 8*7*N
0 = N^4 - 18*N^2 + 56*N - 39
N=1, -5.4414, 2.2207 +/- 1.4953*i

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
re: Unreal!	Ady TZIDON	2018-03-05 05:46:46
re: solution	K Sengupta	2008-07-16 11:47:01
solution	Jason Scott Clark	2007-08-26 12:51:03
Solution	K Sengupta	2007-08-25 23:49:20
Unreal!	Steve Herman	2007-08-25 21:19:16

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