If $\frac{a^2+b^2+c^2-1024}{ab-bc-ca}=-2$ and a + b = 5c, where c > 0, then the value of c is _____.
Answer & explanation
Correct answer: option 1
If $\frac{a^2+b^2+c^2-1024}{ab-bc-ca}=-2$
a + b = 5c
a2 + b2 + c2 - 1024 = -2ab + 2bc + 2ca
= a2 + b2 + c2 + 2ab - 2bc - 2ca = 1024
= (a + b - c)2 = 1024
= a + b - c = 32
Put a + b = 5c
= 5c - c = 32
= 4c = 32
c = 8