The sum of the squares of two positive integers is 208. If the square of the
larger number is 18 times the smaller number, find the numbers.
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The sum of the squares of two positive integers is 208. If the square of the
larger number is 18 times the smaller number, find the numbers.
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Explanation:
Let the smaller number be x. Then,
Square of larger number = 18x
Square of the smaller number = x2
Therefore,
x2+18x=208
x2+18x−208=0
(x+26)(x−8)=0
x=8,−26
But, the numbers are positive.
So, x=8
Hence, the numbers are 8 and 12.
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let larger number be 'x' and the smaller number be 'y'
given that, x² + y² = 208
and x² = 18y
substitute x in
x² + y² = 208
18y + y² = 208
y² + 18y - 208 = 0
(y+26)(y-8) = 0
y = 8 since the numbers are positive.
x² = 18 × 8
x² = 144
x = 12
the numbers are 12 and 8