when we subtract 1 from a number than we get reciprocal of the number. find the number.
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Answered by
2
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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Answered by
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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