Question
A number is more than 21 times its reciprocal by 11/9. What
is the number?Solution
ATQ,
Let the number be x.
x β 21/x = 11/9
β (xΒ² β 21)/x = 11/9
Cross-multiplying:
9xΒ² β 189 = 11x
β 9xΒ² β 11x β 189 = 0
Factorizing:
9xΒ² β 27x + 16x β 189 = 0
9x(x β 3) + 63(x β 3) = 0
(9x + 63)(x β 3) = 0
So, x = β7 or x = 3
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