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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 & Solution
Correct Answer:
Option
A
a + b = 5c
$$\frac{{{a^2} + {b^2} + {c^2} - 1024}}{{ab - bc - ca}} = - 2$$
a2 + b2 + c2 + 2ab - 2bc - 2ac = 1024
(a + b)2 + c(c - 2b - 2a) = 1024
(5c)2 + c[c - 2(b + a)] = 1024
25c2 + c[c - 2 × 5c) = 1024
25c2 - 9c2 = 1024
16c2 = 1024
c2 = 64
c = 8
$$\frac{{{a^2} + {b^2} + {c^2} - 1024}}{{ab - bc - ca}} = - 2$$
a2 + b2 + c2 + 2ab - 2bc - 2ac = 1024
(a + b)2 + c(c - 2b - 2a) = 1024
(5c)2 + c[c - 2(b + a)] = 1024
25c2 + c[c - 2 × 5c) = 1024
25c2 - 9c2 = 1024
16c2 = 1024
c2 = 64
c = 8
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