MathematicsIf (ab-1)2x-1=(ba-1)x-2 then what is the value of x?

If (ab-1)2x-1=(ba-1)x-2 then what is the value of x?


  1. A
    1
  2. B
    2
  3. C
    3
  4. D
    4 

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    Solution:

    Here we are given that (ab-1)2x-1=(ba-1)x-2 and we need to find the value of x
    So firstly we can simplify this equation by opening the bracket and analyse the power of each variable a and b and we must also know that when we have two terms in the power then they are multiplied. For example: If we have (a-1)xthen we can write it as (a-1)x=a-x
    So we can write
    (ab-1)2x-1=(ba-1)x-2
    a2x-1b-(2x-1)=bx-2a-1(x-2)
     a2x-1b-2x+1=bx-2a-x+2−−−−(1)
    Now we have got the left and the right hand side in the simplified form and we need to find the value of x
    So we know that if we are given ax=ay then we can say that x=y by equating the power of the same variable on both sides.
    Similarly equating the power of aa on both the sides in the equation (1) we get that
    2x−1=−x+2
    Upon solving it we get
    2x+x=2+1
    3x=3
    x=1
    Hence we get that x=1
    Now again equating the power of bb on both the sides we get
    2x+1=x2
    2xx=21
    3x=3

    x=1
    Hence we get that the value of x=1
    Hence we can say that option 1 is correct.
     
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