Question

Divide 22 into two parts such that sum of their squares is 314

Answer 1

Step-by-step explanation:

17 and 5 khhhjfuhfdhdkkkdyydky

Answer 2

Given: 22 is divided into two parts such that the sum of their squares is 314.

To find: We have to find the two parts.

Solution:

To determine the numbers we have to follow the below steps as follows-

Let one part of the number be x and another part of the number be 22-x.

Given that the 22 is divided into two parts such that the sum of their squares is 314.

So, we can write-

${x}^{2} + {(22 - x)}^{2} = 314 \\ {x}^{2} + 484 - 44x + {x}^{2} = 314 \\ 2 {x}^{2} - 44x + 170 = 0 \\ {x}^{2} - 22x + 85 = 0 \\ {x}^{2} - 17x - 5x + 85 \\ x(x - 17) - 5(x - 17) = 0 \\ x = 17 \\ x = 5$

The value of x is 17 and 5.

Thus, the numbers are 17 and 5.