Question

Divide 29 into two parts so that the sun of the squares of the parts is 425.Find the value of each Part.

Answer 1

13 and 16

Explanation:

let the 2 parts be x and y, then

x + y = 29 → (1) and

x² + y² = 425 → (2)

From (1) → x = 29 - y → (3)

substitute x = 29 - y into (2)

(29 - y)² + y² = 425 ( expand factor )

841 - 58y + y² + y² = 425 ( rearrange into standard form )

2y² - 58y + 416 = 0 ← in standard quadratic form

divide all terms by 2

y² - 29y + 208 = 0

Consider the factors of 208 which sum to - 29

These are - 13 and - 16, hence

(y - 13)(y - 16) = 0

equate each factor to zero and solve for y

y - 13 = 0 ⇒ y = 13

y - 16 = 0 ⇒ y = 16

substitute these values into (3)

x = 29 - 13 = 16 and x = 29 - 16 = 13

The 2 parts are 13 and 16

Answer 2

The 2 parts are 13 and 16.

Explanation:

WE can set up a system of equations. If the 2 parts are x and y we have:-

x + y = 29

x^2 + y^2 = 425

From the first equation y = 29 - x, so substituting for y in the second equation:-:-

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

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

2x^2 - 58x + 416 = 0

2 (x^2 - 29x + 208) = 0

We need 2 numbers whose sum is 29 and whose product is 208. Yhet are 13 and 16, so:-

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

x = 13, 16

So y = 29-13 , 29 - 16 = 16,13

Thus one number is 13 and the other is 16.