a2 + 9b2 + c2 + 4d2 = 4a + 24b + 6c +4d - 30
⇒ a2 - 4a + 9b2 - 24b + c2 - 6c + 4d2 - 4d +30 = 0
⇒ (a2 - 4a + 4) +(9b2 + 24b + 16) + (c2 - 6c +9) + (4d2 - 4d + 1) = 0
⇒ (a - 2)2 + (3b - 4)2 + (c - 3)2 + 4(d - \(\frac{1}{2}\)) = 0
Which is only possible when,
a - 2 = 0,3b - 4 = 0,c - 3 = 0 and d - \(\frac{1}{2}\) = 0
⇒ a = 2, b = \(\frac{4}{3}\), c = 3 and d = \(\frac{1}{2}\)
Now,
\(\frac{ad}{bc}\) = \(\frac{2\times 1/2}{4/3 \times 3}\) = \(\frac{1}{4}\)
Hence,
The value of \(\frac{ad}{bc}\) = \(\frac{1}{4}\)
