1. Two numbers are such that the
square of greater, one is 504 less than
8 times the square of the other. If the
numbers are in the ratio 3:4, then
find the number.
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Two numbers are such that the square of one is 224 less than 8 times the squared of the other. If the numbers be in the ratio 3:4, what are their values?
Solution: Let the numbers be 4x and 3x.
(3x)^2 = 8*(4x)^2 - 224
9x^2 = 128x^2 - 224
128x^2–9x^2 = 117x^2 = 224, or
x^2 = 224/117
x = ±√(224/117) = ±4√(14/117)
The numbers are ±16√(14/117) and ±12√(14/117). Answer.
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