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3 years ago

If m+1/m= 3, then prove that m^5+1/m^5= 123

Mathematics

1 answer:

Lady_Fox [76]3 years ago

6 0

Step-by-step explanation:

$\qquad\sf {:}\longrightarrow m+\dfrac {1}{m}=3$

$\qquad\sf {:}\longrightarrow m^2+1/m=3$

$\qquad\sf {:}\longrightarrow m^2+1=3m$

$\qquad\sf {:}\longrightarrow m^2-3m+1=0$

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Consider the closed region $V$ bounded simultaneously by the paraboloid and plane, jointly denoted $S$ . By the divergence theorem,

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the volume integral will be much easier to compute. Converting to cylindrical coordinates, we have

$\displaystyle\iiint_V\nabla\cdot\mathbf f(x,y,z)\,\mathrm dV=\iiint_V\mathrm dV$
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$\displaystyle\iint_{S-D}\mathbf f\cdot\mathrm dS=\frac\pi2-\iint_D\mathbf f\cdot\mathrm dS$

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