Question

If the sum of two number is 13 and the sum of their square is 85 then smaller the two number is

Answer 1

Step-by-step explanation:

Let the first number be x and the second number be y.

So,

according to the question,

the sum of numbers = 13

this means,

x + y = 13x+y=13

x = 13 - y \: \: (i)x=13−y(i)

Also,

the sum of squares of numbers = 85

this means,

{x}^{2} + {y}^{2} = 85x2+y2=85

from (i), x = 13 - y

So,

{(13 - y)}^{2} + {y}^{2} = 85(13−y)2+y2=85

169 + {y}^{2} - 26y + {y}^{2} = 85169+y2−26y+y2=85

{2y}^{2} - 26y + 84 = 02y2−26y+84=0

This can be written as

{2y}^{2} - 12y - 14y + 84 = 02y2−12y−14y+84=0

2y(y - 6) - 14(y - 6) = 02y(y−6)−14(y−6)=0

(2y - 14)(y - 6) = 0(2y−14)(y−6)=0

2y - 14 = 0 \: and \: y - 6 = 02y−14=0andy−6=0

y = 7 \: and \:y = 6y=7andy=6

If y = 7,

x = 13 - 7 = 6

If y = 6,

x = 13 - 6 = 7

Hence, the smaller of the two numbers is 6.