Question

A natural number when increased by 84 equals 160 times its reciprocal. find the number.
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Answer 1

Let the natural positive number be x 

ATQ 

x + 84    = 160 ( 1/x) 

x² + 84x = 160 

x² + 84x - 160 = 0 

Here a quadratic equation formed :

Where 

a (coefficient of x²) = 1 

b (coefficient of x ) = 84

c (constant           ) = -160

D (Discriminant    ) = b² - 4ac

                               = 84² - 4 x 1 x 160 

                               = 7056 + 640 

                               = 7696

we are finding roots (zeros) of the quadratic by this quadratic formula

-b+-√D/2a 

Two zeros are 

160 - √7696 / 2  and 160 + √7696 / 2

hope this will help you.

thank you

Answer 2

I hope this may help you