If (a + b) : (b + c) : (c + a) = 7 : 4 : 5 and a + b + c = 16, then (a² + b² + c²) : (ab + bc + ca) is equal toयदि (a + b) : (b + c) : (c + a) = 7 : 4 : 5 एवं a + b + c = 16, तब (a² + b² + c²) : (ab + bc + ca) बराबर होगा

Explanation

Let a + b = 7k, b + c = 4k and c + a = 5k. Adding gives 2(a + b + c) = 16k = 32, so k = 2 and the pairs are 14, 8 and 10, which give c = 2, a = 8 and b = 6. Then a² + b² + c² = 64 + 36 + 4 = 104 and ab + bc + ca = 48 + 12 + 16 = 76, and 104 : 76 = 26 : 19.मान लीजिए a + b = 7k, b + c = 4k और c + a = 5k। जोड़ने पर 2(a + b + c) = 16k = 32, अतः k = 2 और युग्म 14, 8 तथा 10 हैं, जिनसे c = 2, a = 8 और b = 6 मिलते हैं। तब a² + b² + c² = 64 + 36 + 4 = 104 और ab + bc + ca = 48 + 12 + 16 = 76, और 104 : 76 = 26 : 19।