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Is x = √8 ? (1) x^2 − 4√2*x + 8 = 0 (2) x^2 + 2√2 *x − 16 = 0

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Bunuel
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Is x = √8 ? (1) x^2 − 4√2*x + 8 = 0 (2) x^2 + 2√2 *x − 16 = 0 [#permalink] New post   27 Jul 2020, 03:09
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Question Stats:

56% (01:44) correct 44% (01:48) wrong based on 109 sessions
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Is x = √8 ?

(1) x^2 − 4√2*x + 8 = 0
(2) x^2 + 2√2 *x − 16 = 0


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Re: Is x = √8 ? (1) x^2 − 4√2*x + 8 = 0 (2) x^2 + 2√2 *x − 16 = 0 [#permalink] New post   27 Jul 2020, 05:27
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Bunuel wrote:
Is x = √8 ?

(1) x^2 − 4√2*x + 8 = 0
(2) x^2 + 2√2 *x − 16 = 0



Solution


Step 1: Analyse Question Stem


    • We need to find if \( x = \sqrt{8} \)

Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE


Statement 1: \( x^2 − 4√2*x + 8 = 0 \)
    • \( x^2 – 4\sqrt{2}*x + 8 = 0 \)
    • \(⟹ x^2 – 2*2\sqrt{2} + (\sqrt{2})^2 = 0\)
    • \(⟹ (x – 2\sqrt{2})^2 = 0\)
    • \( ⟹ x = 2\sqrt{2} = \sqrt{8}\)
Hence, statement 1 is sufficient and we can eliminate answer Options B, C and E.

Statement 2: \( x^2 + 2√2 *x − 16 = 0 \)
    • \( x^2 + 2√2 *x − 16 = 0 \)
    • \( ⟹ x^2 + 2*\sqrt{2}*x + 2 = 18 \)
    • \( ⟹ ( x + \sqrt{2})^2 = 18 \)
    • \( ⟹ x = -\sqrt{2} + 3\sqrt{2} \space or \space x = -\sqrt{2} - 3\sqrt{2} \)
    • Here we are getting two different values of x.
      o If \( ⟹ x = 2\sqrt{2}⟹ x = \sqrt{8}\)
      o If \( ⟹ x = -\sqrt{2} - 3\sqrt{2} = -4\sqrt{2} ⟹ x≠\sqrt{8}\)
    • The above two results are contradictory.
Hence statement 2 is not sufficient.
Thus, the correct answer is Option A.
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Re: Is x = √8 ? (1) x^2 − 4√2*x + 8 = 0 (2) x^2 + 2√2 *x − 16 = 0 [#permalink] New post   27 Jul 2020, 06:06
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Bunuel wrote:
Is x = √8 ?

(1) x^2 − 4√2*x + 8 = 0
(2) x^2 + 2√2 *x − 16 = 0


Question: Is x = √8 ?

STatement (1) x^2 − 4√2*x + 8 = 0

i.e. \((x- √8)^2 = 0\)
\(x = √8\)

SUFFICIENT

STatement (2) x^2 + 2√2 *x − 16 = 0

i.e. \((x+√2)^2 - 18 = 0\)

i.e. \((x+√2)^2 = 18\)

i.e. \(x+√2 = 3√2\) or \(x+√2 = -3√2\)

i.e. \(x = √8\) YES or \(x = -4√2\) NO

NOT SUFFICIENT

Answer: Option A
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Re: Is x = √8 ? (1) x^2 − 4√2*x + 8 = 0 (2) x^2 + 2√2 *x − 16 = 0 [#permalink] New post   27 Jul 2020, 03:18
Bunuel wrote:
Is x = √8 ?

(1) x^2 − 4√2*x + 8 = 0
(2) x^2 + 2√2 *x − 16 = 0


Statement 1: Sufficient
x^2 − 4√2*x + 8 = 0
=>(x - √8)^2 = 0
=> x = √8, Yes
Statement 2: Insufficient
x^2 + 2√2 *x − 16 = 0
=> (x + 4√2)(x - 2√2) = 0
=> x = 2√2 or -4√2 , may be x = √8

Hence, OA is (A).
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Re: Is x = √8 ? (1) x^2 − 4√2*x + 8 = 0 (2) x^2 + 2√2 *x − 16 = 0 [#permalink] New post   27 Jul 2020, 03:28
Is x = √8 ?

(1) x^2 − 4√2*x + 8 = 0
Compare to a^2+b^2-2ab = 0
(since 2√2x is negative)
A = x
B = 2√2
(X-2√2)^2 = 0
X = 2√2 = √8
Sufficient

(2) x^2 + 2√2 *x − 16 = 0
Compare to a^2+b^2+2ab = 0 (since 2√2x is positive)
x^2 + 2√2 *x +2 -2 − 16 = 0
A = x
B = √2

(X+√2)^2-(3√2)^2 = 0
A^2-B^2 = (A+B)(A-B)
(X+√2+3√2)(X+√2-3√2) = 0
(X+4√2)(x-2√2) = 0
X = √8 or x = -√32
(Insufficient)

Answer is A

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Re: Is x = √8 ? (1) x^2 − 4√2*x + 8 = 0 (2) x^2 + 2√2 *x − 16 = 0 [#permalink] New post   27 Jul 2020, 04:49
Statement 1 is sufficient.
Statement 2 returns two values for X.

Answer - A

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Re: Is x = √8 ? (1) x^2 − 4√2*x + 8 = 0 (2) x^2 + 2√2 *x − 16 = 0 [#permalink] New post   27 Jul 2020, 07:36
We need to find if x = √8?

Statements:

(1) x^2 − 4√2*x + 8 = 0
Solving, we have
x^2 − (2)(x)(2√2) + (2√2)^2 = 0
(x-2√2)^2 = 0
Therefore, x = 2√2 = √8
Sufficient

(2) x^2 + 2√2 *x − 16 = 0
Solving we get,
x^2 + (2)(√2)(x) − 16 = 0
x^2 + (2)(√2)(x) +2 - 2 - 16 = 0
(x+√2)^2 = 18
x+√2 = +-√18 = +-3√2
Therefore, x = 2√2 = √8 or x = -4√2
Insufficient

Hence, the answer is Option (A)
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Re: Is x = √8 ? (1) x^2 − 4√2*x + 8 = 0 (2) x^2 + 2√2 *x − 16 = 0 [#permalink]
27 Jul 2020, 07:36
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Bunuel
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