Find x+y+z if $x^2+xy+y^2=a^2$, $y^2+yz+z^2=b^2$ and $z^2+zx+x^2=c^2$
86398
Given six numbers $x,y,z,a,b,c$ which satisfy the following relations. Express $x+y+z$ in terms of $a,b,c$
94831
Finding value of $a +b+c$
41689
Find all solutions: $x^2 + 2y^2 = z^2$
83496
Math contest integer triplet problem: $x + y + z + xy + yz + xz = xyz − 1$
135742
Solve system of simultaneous equations in $3$ variables: $x+y+xy=19$, $y+z+yz=11$, $z+x+zx=14$
33105
Find the value of $a^2-b^2+c^2$
147442
Quadratic Diophantine Equation $x^2 + axy + y^2 = z^2$
17100
Prove that $\frac{b^2+c^2}{b+c}+\frac{c^2+a^2}{c+a}+\frac{a^2+b^2}{a+b} \ge a+b+c$
73538
solving $\cos z + \sin z = i$
71756
diophantine equation: $x^2 +y^2 = z^n$
121353
If $x$ and $y$ are not both $0$ then $ x^2 +xy +y^2> 0$
88760
Find the integral solutions to $ x^2+y^2+z^2=x^2y^2$
18313
show this inequality with $xy+yz+zx=3$
18203
Diophantine equation $a^2+b^2=c^2+d^2$
27911
How can I prove that $xy\leq x^2+y^2$?
41226
Find $f:f(xf(x)+f(y))=f(x)^2+y$
120736
If xy + yz + zx = 1, ...........