Respuesta :
Answer:
13 and 16
Step-by-step 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:
The 2 parts are 13 and 16.
Step-by-step 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.
