1/(2vx + vx) = 1/(3vx)
Ans A
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In the posted problem, v = √.
Here is the problem with the intended notation:
(√x + √y)(√x - √y) = x-y.
Thus:
1 / [√(2x) + √x]
= 1 / (√x)(√2+1)
= (1)(√2-1) / (√x)(√2+1)(√2-1)
= (√2-1) / (√x)(2-1)
= (√2-1) / √x
The correct answer is D.
Here is the problem with the intended notation:
Note the following:If x>0, then 1 / [√(2x) + √x] =
A. 1 / √(3x)
B. 1/ 2√(2x)
c. 1 / x√2
D. (√2-1) / √x
E. (1+√2) / √x
(√x + √y)(√x - √y) = x-y.
Thus:
1 / [√(2x) + √x]
= 1 / (√x)(√2+1)
= (1)(√2-1) / (√x)(√2+1)(√2-1)
= (√2-1) / (√x)(2-1)
= (√2-1) / √x
The correct answer is D.
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Quick approach
If x>0, then 1 / [√(2x) + √x] = 1 / [√(2) + √1] = 1 / [√(2) + 1]
Given : X>0
Put X =1 & look for answer choice that matches with above value .
A. 1 / √(3) NO ( √(3) =1.723 √(2) + 1 = 1.414+1 = 2.414 )
B. 1/ 2√(2) NO (2√(2) is not equal to √(2) + 1 )
c. 1 / √2 NO ( √2 is not equal to √(2) + 1 )
D. (√2-1) / √1 Yes (written after factorizing the denominator)
E. (1+√2) / √1 NO Clearly this is > 1 and our value is < 1 as 1/2.414 is <1
If x>0, then 1 / [√(2x) + √x] = 1 / [√(2) + √1] = 1 / [√(2) + 1]
Given : X>0
Put X =1 & look for answer choice that matches with above value .
A. 1 / √(3) NO ( √(3) =1.723 √(2) + 1 = 1.414+1 = 2.414 )
B. 1/ 2√(2) NO (2√(2) is not equal to √(2) + 1 )
c. 1 / √2 NO ( √2 is not equal to √(2) + 1 )
D. (√2-1) / √1 Yes (written after factorizing the denominator)
E. (1+√2) / √1 NO Clearly this is > 1 and our value is < 1 as 1/2.414 is <1
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