Question

when we subtract 1 from a number than we get reciprocal of the number. find the number.​

Answer 1

Answer:

x = 1 + 1/x

Multiply both sides by x:

x2 = x + 1

x2 - x - 1 = 0

Use the quadratic formula:

x = 1/2 ± (1/2)√((-1)2-4(1)(-1))

x = (1±√5)/2

Now √5 >1, so x is only positive when it's :

x = (1+√5)/2

Now let's check if it's right:

x = 1/x + 1

x - 1 = 1/x

Substitute (1+√5)/2 for x:

(1+√5)/2 - (2/2) = 2/(1+√5)

Multiply the numerator and denominator of the RHS by the conjugate of the denominator:

(√5 - 1)/2 = (2/(1+√5))*(1-√5)/(1-√5)

(√5 - 1)/2 = 2*(1-√5)/-4

(√5 - 1)/2 = (√5 - 1)/2

Yup, it seems to be true!

Step-by-step explanation:

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Answer 2

Answer:

Step-by-step explanation:

Let the number be x

A/Q

x - 1 = 1/x

x = 1/x + 1

x = 1 + 1x /x

x^ = 1 + 1x

x^ - 1x + 1 =0

...

Hence you can solve this

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