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Let the number be x.

The reciprocal of a number is simply 1/the number so the reciprocal of x is 1/x.

4 times the reciprocal is 4(1/x) which is (4/x)

But the number exceeds it by 3, or in other words it is 3 greater than it

So the equation you end up with is:

(4/x) + 3 = x

4 + 3x = x^2 ...... multiply both sides by x

x^2 - 3x - 4 = 0

(x - 4)(x + 1) = 0 .... factorize

so x = 4 or x = -1

we have two values because we multiplied by x earlier. But one of these values is false.

So test them yourself by substituting each value for x into the first equation.

You will see that the right answer is x= 4

the required number = x

reciprocal of required number = 1/x

4 times the reciprocal = 4(1/x)

according to the question,

x = 4(1/x) +3

x = 4/x +3

x =( 4 + 3x) / x by taking the lcm

x² = 4 + 3x

x²- 3x -4 =0 by cross multiplying

x²-4x +x - 4 = 0

x(x-4)+1(x-4) = 0

(x+1)(x-4) = 0

x = -1, x = 4

the required no.= x = -1 and 4