Divide 29 into two parts so that the sum of the squares of the parts i

1.	Divide 29 into two parts so that the sum of the squares of the parts is 425.
Answer» Let’s assume that one part is (x), so the other part will be (29 – x). From the question, the sum of the squares of these two parts is 425. Expressing the same by equation we have, x² + (29 – x)² = 425 ⇒ x²+ x²+ 841 + -58x = 425 ⇒ 2x²– 58x + 841 – 425 = 0 ⇒ 2x²– 58x + 416 = 0 ⇒ x²– 29x + 208 = 0 Solving for x by factorization method, we get x²– 13x – 16x + 208 = 0 ⇒ x(x – 13) – 16(x – 13) = 0 ⇒ (x – 13)(x – 16) = 0 Now, either x – 13 = 0 ⇒ x = 13 Or, x – 16 = 0 ⇒ x = 16 Thus, the two parts whose sum of the squares is 425 are 13 and 16 respectively.

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

Answer»

Let’s assume that one part is (x), so the other part will be (29 – x).

From the question, the sum of the squares of these two parts is 425.

Expressing the same by equation we have,

x² + (29 – x)² = 425

⇒ x²+ x²+ 841 + -58x = 425

⇒ 2x²– 58x + 841 – 425 = 0

⇒ 2x²– 58x + 416 = 0

⇒ x²– 29x + 208 = 0

Solving for x by factorization method, we get

x²– 13x – 16x + 208 = 0

⇒ x(x – 13) – 16(x – 13) = 0

⇒ (x – 13)(x – 16) = 0

Now, either x – 13 = 0 ⇒ x = 13

Or, x – 16 = 0 ⇒ x = 16

Thus, the two parts whose sum of the squares is 425 are 13 and 16 respectively.