Show that x³ + y³ + z³ - 3xyz is a multiple of x+y+z

Mathematics

1 answer:

White raven [17]2 years ago

7 0

x³ + y³ + z³ - 3xyz is a multiple of x+y+z.

<h3>What is a multiple?</h3>

It should be noted that a multiple simply means a number that van be divided by another a certain number if times without a remainder.

Put x + y + z = 0

= x³ + y³ + z³ - 3xyx

= 0(x² + y² + z² - xt - yz - zx)

= x³ + y³ + z³ - 3xyz = 0.

x³ + y³ + z³ = 3xyz

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$\bf \qquad \qquad \textit{direct proportional variation}\\\\
\textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby 
\begin{array}{llll}
k=constant\ of\\
\qquad variation
\end{array}\\\\
-------------------------------\\\\
\begin{array}{llll}
\stackrel{frequency}{f}\textit{ of a vibrating string varies directly}\\
\qquad \qquad \textit{with the square root of the tension }\stackrel{tension}{t}
\end{array}$

$\bf f=k\sqrt{t}\quad \textit{we also know that }
\begin{cases}
f=300\\
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\end{cases}\implies 300=k\sqrt{8}
\\\\\\
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\\\\\\
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$\bf thus\qquad f=\stackrel{k}{75\sqrt{2}}\sqrt{t}\implies \boxed{f=75\sqrt{2t}}\\\\
-------------------------------\\\\
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3 years ago

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Step-by-step explanation:

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