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If x is an integer and   what is the value of x?
  • a)
    -3
  • b)
    -1
  • c)
    0
  • d)
    2
  • e)
    3
Correct answer is option 'E'. Can you explain this answer?
Verified Answer
If x is an integer and what is the value of x?a)-3b)-1c)0d)2e)3Correct...
Given equation is
And, we need to find the value of x, given that x is an integer.
Step 2 & 3: Finding required values and calculating the final answer
Let us rewriting the last term of (I) to get x-1 in the denominator:
Let us now bring the terms with the same denominator together:
  • (x + 1)2 = {2(x – 1)}2
  • [(x+1)2-{2(x-1)}2 ]=0 ………….. (II)
  • Observe that this is of the form  a2 – b2 = (a+b)(a-b)
     
    So let us say:
    a = x + 1             
    b = 2(x – 1) = 2x - 2
     
    Therefore:
    a + b = x + 1 + 2x – 2 = 3x -1
    a – b = x + 1 - 2x + 2 = -x + 3
     
    Therefore we can rewrite (II) as:
    (3x-1)(3-x)=0
  • Putting each factor to zero:
Since it is given that x is an integer,
Thus, x = 3 is the required answer.
 
Answer: Option (E)
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