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# If x and y are positive numbers, √x + √y = 6 and xy = 4, then what is

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Re: If x and y are positive numbers, √x + √y = 6 and xy = 4, then what is [#permalink]
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If $$x$$ and $$y$$ are positive numbers, $$√x+√y=6$$ and $$xy=4$$, then what is the value of $$x+y$$ ?

$$√x+√y=6$$
Square the both sides: $$(√x+√y)^{2}=6^{2}$$
--> $$x+ y +2√(xy) = 36$$

$$x+ y = 36 -2√(xy) = 36 -2√4= 36-4= 32$$

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If x and y are positive numbers, √x + √y = 6 and xy = 4, then what is [#permalink]
√x+√y=6
xy=4
square both sides
√x+√y=6
x+y+2√xy=36
x+y+2√4= 36
x+y+4=36
x+y=32
IMO C

If x and y are positive numbers, √x+√y=6 andxy=4, then what is the value of x+y ?

A. 2
B. 28
C. 32
D. 34
E. 36

Originally posted by Archit3110 on 09 Mar 2020, 08:22.
Last edited by Archit3110 on 10 Mar 2020, 07:32, edited 1 time in total.
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Re: If x and y are positive numbers, √x + √y = 6 and xy = 4, then what is [#permalink]
1
Kudos
If x and y are positive numbers, √x+√y=6 and xy=4, then what is the value of x+y ?

A. 2
B. 28
C. 32
D. 34
E. 36

$$(√x+√y)^2 = 6^2$$
x + y + 2√x√y = 36
x + y = 36 - 2.√4
x + y = 36 - 4 = 32

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Re: If x and y are positive numbers, √x + √y = 6 and xy = 4, then what is [#permalink]
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If x and y are positive numbers, √x+√y=6√x+√y=6 and xy=4xy=4, then what is the value of x+yx+y ?

A. 2
B. 28
C. 32
D. 34
E. 36

x + 2\sqrt{xy}+ y = 36
x + 2. 2 (for square root, we consider only the positive value) +y = 36
x + y = 32.

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Re: If x and y are positive numbers, √x + √y = 6 and xy = 4, then what is [#permalink]
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Kudos
(√x + √y)^2 = 36
x+2$$\sqrt{xy}$$+y = 36

substitute in xy = 4

x+ y + 4 = 36
x + y = 32

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If x and y are positive numbers, √x + √y = 6 and xy = 4, then what is [#permalink]
Quote:
If x and y are positive numbers, √x+√y=6 and xy=4, then what is the value of x+y?

A. 2
B. 28
C. 32
D. 34
E. 36

√x+√y=6
(√x+√y)^2=6^2
x+y+2√xy=36
x+y=36-2(√4)
x+y=36-4=32

Ans (C)

Originally posted by exc4libur on 09 Mar 2020, 17:38.
Last edited by exc4libur on 10 Mar 2020, 08:36, edited 1 time in total.
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Re: If x and y are positive numbers, √x + √y = 6 and xy = 4, then what is [#permalink]
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Kudos
x + y = (√x+√y)^2 - 2√(xy) = 36 - 2√4 = 36 - 4 = 32

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Re: If x and y are positive numbers, √x + √y = 6 and xy = 4, then what is [#permalink]
1
Kudos
If x and y are positive numbers, √x+√y=6 and xy=4, then what is the value of x+y ?

A. 2
B. 28
C. 32
D. 34
E. 36

Given that,
√x+√y=6
(√x+√y)^2=6^2 ( Squaring to the both sides)
Or, x + 2√xy+ y = 36
Or, x + y + 2√xy = 36
Or, x + y + 2*2 = 36( Putting xy =4)
Or, x + y = 32

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Re: If x and y are positive numbers, x + y = 6 and xy = 4, then what is [#permalink]
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Re: If x and y are positive numbers, x + y = 6 and xy = 4, then what is [#permalink]
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