Summing Quadratic Forms in Three Variables: True or False?

MikeDietrich
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Homework Statement


True or False and Why?

"The sum of two quadratic forms in three variables must be a quadratic form as well."


Homework Equations


q(x_1,x_2,x_3)=x_1^2+x_2^2+x_3^2+x_1x_3+x_2x_3



The Attempt at a Solution


I am definitely missing something. To me this is a "duh" statement (and I am sure it's not). If I sum two equations in quadratic form then naturally the answer will be in the quadratic form. Any hints appreciated.
 
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Yes, the answer looks quite trivial...
 
Are you dealing with quadratic forms associated with matrices?

<br /> x&#039; A x<br />

If so, you probably need to take that into account.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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