Question

prove that if a+1/b=1, b+1/c=1 then c+1/a=1.​

Answer 1

Answer:

Step-by-step explanation:

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If A+1/B=1 and B+1/C=1, then what is the value of C+1/A=?

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7 Answers

Pra Shanthi

Pra Shanthi, Faculty at Bright Future Academy

Answered Mar 20, 2018

A+1\B=1——————(1)

B+1\C=1———————(2)

B=1–1\C

Substituting in (1),we get

A+C/(C-1)=1

On cross multiplication, AC-A+C=C-1

Thus AC-A=-1 or A=1\(C+1)——————-(3)

Now , C+1\A=C+C+1=2C+1=2C+2–1=2(C+1)-1=(2\A)-1 from (3)

=(2\(1–1\B))-1

Answer 2

Answer:

a + 1/b = 1

=>(a b + 1)/b = 1

a b + 1 = b

b – a b = 1

b (1 – a) = 1

b = 1/(1 – a) ………………………… (1)

b + 1/c = 1

From equation (1), b = 1/(1 – a)

1/(1 – a) + 1/c = 1

(c + 1 – a)/c (1 – a) = 1

c – a + 1 = c – c a

– a + 1 = – c a

a – c a = 1

a (1 – c) = 1

a = 1/(1 – c)

Now, the value of c + 1/a

Put the value of a = 1/(1 – c)

Then, c + 1/{1/(1 – c) }

= c + 1 – c

= 1

Thus, the value of c + 1/a = 1

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