Question

Two positive whole numbers differ by 5 and the sum of their squares is 193. Find the two numbers.

Answer 1

Answer:

the value of x sq is 84 and y sq is 109 l hope it may help you

Answer 2

Step-by-step explanation:

suppose the 2 positive numbers are x and y.

$x > y$

suppose

$sum \: of \: there \: squre \: is \: {x}^{2} + {y}^{2} . \\ then \\ {x}^{2} + {y}^{2} = 193.$

$x - y = 5 \\ {(x - y)}^{2} = 25 \\ {x}^{2} + {y}^{2} - 2xy = 25 \\ 193 - 2xy = 25 \\ 2xy = 193 - 25 \\ 2xy = 168 \\ xy = 84 \\ (y + 5)y = 84 \\ {y}^{2} + 5y - 84 = 0 \\ {y}^{2} + 12y - 7y - 84 = 0 \\ y(y + 12) - 7(y + 12) = 0 \\ (y - 7)(y + 12) = 0$

$y = 7. \: and \: y = - 12 \\ y = 7 \\ x = y + 5 \\ x = 7 + 5 \\ x = 12$