Question

The sum of two numbers is 13 and the sum of their squares is 85 the smaller of the two number is

Answer 1

y is 6 and x is 7 x+y=13 and x^2+y^2=85 solve two equations

Answer 2

Given:

The sum of two numbers is 13 and the sum of their squares is 85.

To find:

The smaller of the two numbers.

Solution:

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

So,

according to the question,

the sum of numbers = 13

this means,

$x + y = 13$

$x = 13 - y \: \: (i)$

Also,

the sum of squares of numbers = 85

this means,

${x}^{2} + {y}^{2} = 85$

from (i), x = 13 - y

So,

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

$169 + {y}^{2} - 26y + {y}^{2} = 85$

${2y}^{2} - 26y + 84 = 0$

This can be written as

${2y}^{2} - 12y - 14y + 84 = 0$

$2y(y - 6) - 14(y - 6) = 0$

$(2y - 14)(y - 6) = 0$

$2y - 14 = 0 \: and \: y - 6 = 0$

$y = 7 \: and \:y = 6$

If y = 7,

x = 13 - 7 = 6

If y = 6,

x = 13 - 6 = 7

Hence, the smaller of the two numbers is 6.