# Divide 29 into 2 parts so that the sum of the squares of the parts is 425 ..... Find the parts

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Let the two parts be x and y

x + y = 29 ⇒ y = 29 - x

so according to question x² + y² = 425

⇒ x² + (29 - x)² = 425

⇒ x² + 841 + x² - 58x = 425

⇒2x² - 58x + 416 = 0

⇒ x² - 29x + 208 = 0

⇒ x² - 13x - 16x + 208 = 0

⇒ x(x - 13) - 16(x - 13) = 0

⇒ (x - 16)(x - 13) = 0

so x = 16 or 13__ANSWER__

x + y = 29 ⇒ y = 29 - x

so according to question x² + y² = 425

⇒ x² + (29 - x)² = 425

⇒ x² + 841 + x² - 58x = 425

⇒2x² - 58x + 416 = 0

⇒ x² - 29x + 208 = 0

⇒ x² - 13x - 16x + 208 = 0

⇒ x(x - 13) - 16(x - 13) = 0

⇒ (x - 16)(x - 13) = 0

so x = 16 or 13

x + y = 29

y = 29 - x

A.T.Q

x² + y² = 425

x² + (29 - x)² = 425

x² + 841 + x² - 58x = 425

2x² - 58x + 416 = 0

x² - 29x + 208 = 0

By quadratic formula

D=b²-4ac

=841-832= 9

Now x=

2a 2a

x

2 2