Question

Divide 29 two parts so that the sum of the squares of the parts is 425

Answer 1

Let the first part be x.
Therefore, second part = 29 - x
According to the given condition, sum of the squares of two parts is 425.
⇒ x2 + (29-x)2 = 425
⇒ x2 + 841- 58x + x2 = 425
⇒ 2x2 -58x + 416 = 0
⇒ x2 - 29x + 208 = 0
⇒ (x - 13) (x - 16) = 0
⇒ x = 13, 16
When, first part is 13, then second part = 29 - 13 = 16
Similarly, when, first part is 16, then second part = 29 - 16 = 13
Therefore, the two parts are: (13, 16) or (16, 13).

Answer 2

Answer:

Let the two parts be x and 29-x

Then by hypothesis,we have

x^2+(29-x)^2=425

x^2+841+x^2-58x=425

2x^2-58x+416=0

x^2-29x+208=0

x^2-16x-13x+208=0

x(x-16)-13(x-16)=0

(x-16)(x-13)=0

Either

x=16 or x=13

Step-by-step explanation: