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20 Aug 2021, 08:07
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
63% (02:34) correct
37%
(02:58)
wrong
based on 276
sessions
History
Date
Time
Result
Not Attempted Yet
20 Aug 2021, 16:04
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x^(1/2) means the square root of x.
Similarly, (3-x)^(1/2) means the square root of (3-x).
therefore, square root of (3-x) = square root of x +1
Squaring both the sides, we get:
3-x=x+1+2*[(x)^1/2]
On solving we get:
2 - 2x = 2*[(x)^1/2]
2(1-x)=2*[(x)^1/2]
cancelling 2 on both sides:
1-x=(x)^1/2
Now, squaring both sides again:
1+x^2-2x=x
1+x^2=3x
x^2=3x-1
Therefore, 4(x^2)= 4(3x-1)
= 12x-4
Answer is E.
Similarly, (3-x)^(1/2) means the square root of (3-x).
therefore, square root of (3-x) = square root of x +1
Squaring both the sides, we get:
3-x=x+1+2*[(x)^1/2]
On solving we get:
2 - 2x = 2*[(x)^1/2]
2(1-x)=2*[(x)^1/2]
cancelling 2 on both sides:
1-x=(x)^1/2
Now, squaring both sides again:
1+x^2-2x=x
1+x^2=3x
x^2=3x-1
Therefore, 4(x^2)= 4(3x-1)
= 12x-4
Answer is E.
General Discussion
21 Aug 2021, 09:07
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MonkeyDDes
Square both sides to get:
\(3 - x = x + 2*\sqrt{x} + 1\)
Then isolate \(2\sqrt{x}\) to get: \(2\sqrt{x}= 2 - 2x\)
Square one more time to get \(4x = 4x^2 - 8x + 4\). Thus \(4x^2 = 12x - 4\).
Note A and B must be wrong as this equation has two unique solutions.
Ans: E
