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705-805 (Hard)|   Exponents|   Roots|      
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MonkeyDDes
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If (3-x)^(1/2) = (x)^(1/2) + 1, then 4x²= 20 Aug 2021, 08:07
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E
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Difficulty:

75% (hard)

Question Stats:

61% (02:37) correct 39% (02:51) wrong based on 368 sessions

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If (3-x)^(1/2) = (x)^(1/2) + 1, then 4x²=

A.2
B.4
C.x
D.x-6
E.12x-4
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E
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ShifaliGupta
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If (3-x)^(1/2) = (x)^(1/2) + 1, then 4x²= 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.
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TestPrepUnlimited
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If (3-x)^(1/2) = (x)^(1/2) + 1, then 4x²= 21 Aug 2021, 09:07
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MonkeyDDes
If (3-x)^(1/2) = (x)^(1/2) + 1, then 4x²=

A.2
B.4
C.x
D.x-6
E.12x-4
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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
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If (3-x)^(1/2) = (x)^(1/2) + 1, then 4x²= 16 Jul 2024, 04:45
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­↧↧↧ Detailed Video Solution to the Problem Series ↧↧↧



Given that (3-x)^(1/2) = (x)^(1/2) + 1 and we need to find the value of \(4x²\)

Lets square both the sides, we get

\(((3-x)^(1/2))^2 = ((x)^(1/2) + 1)^2\)
=> 3 - x = x + 2*\(\sqrt{x}\) * 1 + 1^2 = x + 2*\(\sqrt{x}\) + 1
=> 3 - x - x - 1 = 2*\(\sqrt{x}\)
=> 2 - 2x = 2*\(\sqrt{x}\)

Divide by 2 on both the sides
=> 1 - x = \(\sqrt{x}\)

Square both the sides
=> 1 -2*1*x + \(x^2\) = \((\sqrt{x})^2\)
=> 1 - 2x + \(x^2\) = x
=> \(x^2\) = x + 2x - 1 = 3x - 1
=> 4\(x^2\) = 4*(3x-1) = 12x - 4

So, Answer will be E
Hope it helps!

Watch the following video to MASTER Roots

­
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If (3-x)^(1/2) = (x)^(1/2) + 1, then 4x²= 26 Oct 2025, 07:49
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