Find the value of M

**Dragon** · January 30th 2007, 03:38 PM

If m+n=3 and m^2+N^2=6 find the numerical value for m^3+N^3

**ThePerfectHacker** · January 30th 2007, 04:55 PM

Originally Posted by Dragon

If m+n=3 and m^2+N^2=6 find the numerical value for m^3+N^3

You are told that,
$n+m=3$
Thus, squaring
$(n+m)^2=9$
$n^2+2nm+m^2=9$
Thus,
$2mn+6=9$
Thus,
$2 mn=3 \,$
$mn=1.5$ .

Thus,
$n^3+m^3=(n+m)(n^2-nm+m^2)=(3)(6-1.5)$

**Soroban** · January 30th 2007, 09:14 PM

Hello, Dragon!

Another approach . . .

If $m+n\,=\,3$ and $m^2+n^2\,=\,6$ ,
find the numerical value for $m^3+n^3$

We are given: . $\begin{array}{cc}(1)\\(2)\end{array} \begin{array}{cc}m + n \:=\:3 \\ m^2+n^2\:=\:6\end{array}$

Square (1): . $(m + n)^2\:=\:3^2$

. . . . . . . . . $\underbrace{m^2 + n^2} + 2mn\:=\:9$
. . . . . . . . . - - $\downarrow$
Substitute (2): . $6 + 2mn \:=\:9\quad\Rightarrow\quad mn \,=\,\frac{3}{2}\quad(3)$

Cube (1): . $(m+n)^3\:=\:3^3\quad\Rightarrow\quad m^3 + 3m^2n + 3mn^2 + n^3\:=\:27$

. . . . . . . $\text{and we have: }\;\;m^3 + n^3 + 3\underbrace{mn}\underbrace{(m + n)}\:=\:27$
. . . . . . . . . . . . . . . . . . . . . . . . . . $\downarrow\quad\;\downarrow$
Substitute (3) and (1): . $m^3 + n^3 + 3\left(\frac{3}{2}\right)(3)\:=\:27$

Therefore: . $m^3+n^3\:=\:\frac{27}{2}$

Math Help - Find the value of M

LinkBack

Thread Tools

Display

Find the value of M

Similar Math Help Forum Discussions

Find an Equation of the Tangent Line to the parabola at the given point and find....

Given 3 points, find the area of the triangle/find the volume of the parallelepiped

How to find the find local max, min and inflection points from an integral?

Find condition that wedge may move and if it does, find acceleration?

Have dv/dx need to find dx/dt ? (have velocity w/ respect displace - find Accel?)