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in Quadratic Equations by (48.0k points)
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The difference between the quotients when 192 is divided by two numbers one of which is a square of the other is 21. The numbers are :

(a) 4, 16

(b) 16, 256

(c) 9, 81

(d) 8, 64

1 Answer

+1 vote
by (49.1k points)
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Best answer

Correct option is (d) 8, 64

Let the smaller number be x.

Hence

\(\frac{192}x - \frac{192}{x^2} = 21\)

192x − 192 = 21x2

21x2 − 192x + 192 = 0

7x2 − 64x + 64 = 0

(x − 8)(7x − 8) = 0

Hence the number has to be a integer.

Therefore

x = 8

Hence its square is 82 = 64.

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