Question

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

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Answer 1

13 and 16.

Explanation:

Let the 2 parts be x and y, then:

x + y = 29

x^2 + y^2 = 425

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

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

x^2 + 841 - 58x + x^2 - 425 = 0

2x^2 - 58x + 416

x^2 - 29x + 208 = 0

208 = 2*2*2*2*13

= 16 * 13

So factoring we get:

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

x = 13 ,16

So the numbers are 13 and 16.