If the sum of two numbers is 13 and the sum of their square is 85. Find the numbers?
(A) 6 & 7
(B) 5 & 8
(C) 4 & 9
(D) 3 & 10
Answer: (A)
Explanation: Let the numbers be x and 13-x
Then x2 + (13 – x)2 = 85
∴ x2 + 169 + x2 – 26x = 85
∴ 2 x2 – 26x + 84 = 0
∴ x2 – 13x + 42 = 0
∴ (x-6)(x-7)=0
Hence numbers are 6 & 7