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

2
by akshaysunil73

2014-11-03T21:29:01+05:30

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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

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which one?
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2014-11-04T06:42:12+05:30
Let the two parts be x and y
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

D=b²-4ac
=841-832= 9

Now x=  -b + √D   or     -b - √D
2a                   2a

x
= 29 + 3      or      29 - 3
2                      2

x= 32    or     26
2              2

x= 16      or    x=   13