Maths Question

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February 3rd 2008, 11:17 PM
acevipa

Maths Question

I'm having trouble working out this question. Could someone please provide working on how to solve this.

If $2x = a + b + c$ , show that $(x-a)^2 + (x-b)^2 + (x-c)^2 + x^2 = a^2 + b^2 + c^2$
February 3rd 2008, 11:46 PM
mr fantastic

Quote:

Originally Posted by acevipa

I'm having trouble working out this question. Could someone please provide working on how to solve this.

If $2x = a + b + c$ , show that $(x-a)^2 + (x-b)^2 + (x-c)^2 + x^2 = a^2 + b^2 + c^2$

There are elegant ways and brutal ways ......

Brutal:

1. Sub $x = \frac{a}{2} + \frac{b}{2} + \frac{c}{2}$ into $(x-a)^2 + (x-b)^2 + (x-c)^2 + x^2$ .

2. Expand the above.

3. Simplify the above.
February 4th 2008, 12:20 AM
mr fantastic

Quote:

Originally Posted by acevipa

I'm having trouble working out this question. Could someone please provide working on how to solve this.

If $2x = a + b + c$ , show that $(x-a)^2 + (x-b)^2 + (x-c)^2 + x^2 = a^2 + b^2 + c^2$

And elegant:

$(x-a)^2 + (x-b)^2 + (x-c)^2 + x^2 = x^2 - 2ax + a^2 + x^2 - 2bx + b^2 + x^2 - 2cx + c^2 + x^2$

$= a^2 + b^2 + c^2 + 4x^2 -2x(a + b + c)$ .

Substitute $a + b + c = 2x$ :

$= a^2 + b^2 + c^2 + 4x^2 -4x^2 = a^2 + b^2 + c^2$ .

Let your mood decide which way is for you.

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