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Omni-MATH / Knowing that the system

Problem

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problem

Knowing that the system x+y+z=3,x + y + z = 3,x3+y3+z3=15,x^3 + y^3 + z^3 = 15,x4+y4+z4=35,x^4 + y^4 + z^4 = 35, has a real solution x,y,zx, y, z for which x2+y2+z2<10x^2 + y^2 + z^2 < 10, find the value of x5+y5+z5x^5 + y^5 + z^5 for that solution.
Plain-text mathematical notation (without MathML)
Knowing that the system
x+y+z=3,x³+y³+z³=15,x⁴+y⁴+z⁴=35,
has a real solution x,y,z for which x²+y²+z²<10, find the value of x⁵+y⁵+z⁵ for that solution.
Original LaTeX notation
Knowing that the system
\[x + y + z = 3,\]\[x^3 + y^3 + z^3 = 15,\]\[x^4 + y^4 + z^4 = 35,\]
has a real solution $x, y, z$ for which $x^2 + y^2 + z^2 < 10$, find the value of $x^5 + y^5 + z^5$ for that solution.

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Source and history

task_id
b524e8a5-97b4-5449-b365-8e61a668872b
task_key
test--b524e8a5-97b4-5449-b365-8e61a668872b
task_revision_id
1
config / split
/ test

Official source

initial import