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# If x^2 + y^2 = 2ab and 2xy = a^2 + b^2, with a, b, x, y > 0, then x +

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Math Expert
Joined: 02 Sep 2009
Posts: 50658
If x^2 + y^2 = 2ab and 2xy = a^2 + b^2, with a, b, x, y > 0, then x +  [#permalink]

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31 May 2017, 00:38
00:00

Difficulty:

15% (low)

Question Stats:

81% (01:18) correct 19% (02:28) wrong based on 103 sessions

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If $$x^2 + y^2 = 2ab$$ and $$2xy = a^2 + b^2$$, with a, b, x, y > 0, then x + y =

(A) ab

(B) a – b

(C) a + b

(D) $$\sqrt{a^2 + b^2}$$

(E) $$\sqrt{a^2 − b^2}$$

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Joined: 26 Jul 2016
Posts: 36
Location: India
Re: If x^2 + y^2 = 2ab and 2xy = a^2 + b^2, with a, b, x, y > 0, then x +  [#permalink]

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31 May 2017, 01:38
1
1
x^2 + y^2 = 2ab-------- (1)
2xy = a^2 + b^2-------- (2)
(1)+(2) => x^2 + y^2 +2xy = a^2 + b^2+2ab
(x+y)^2=(a+b)^2
(x+y)=(a+b)
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Joined: 04 Dec 2015
Posts: 715
Location: India
Concentration: Technology, Strategy
Schools: ISB '19, IIMA , IIMB, XLRI
WE: Information Technology (Consulting)
Re: If x^2 + y^2 = 2ab and 2xy = a^2 + b^2, with a, b, x, y > 0, then x +  [#permalink]

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31 May 2017, 15:02
1
1
Bunuel wrote:
If $$x^2 + y^2 = 2ab$$ and $$2xy = a^2 + b^2$$, with a, b, x, y > 0, then x + y =

(A) ab

(B) a – b

(C) a + b

(D) $$\sqrt{a^2 + b^2}$$

(E) $$\sqrt{a^2 − b^2}$$

$$x^2 + y^2 = 2ab$$ -------------(i)
$$2xy = a^2 + b^2$$ -------------(ii)

We get;

$$x^2 + y^2 +2xy = a^2+b^2+2ab$$
$$(x+y)^2 = (a+b)^2$$

Therefore; x+y = a+b
Intern
Joined: 25 Apr 2016
Posts: 25
Concentration: Entrepreneurship, Marketing
Re: If x^2 + y^2 = 2ab and 2xy = a^2 + b^2, with a, b, x, y > 0, then x +  [#permalink]

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31 May 2017, 18:45

Given:- x^2 + y^2 = 2ab
and 2xy = a^2 + b^2

(x+y)^2 = x^2 + y^2 + 2xy (standard formula)

Substituting:-

a^2 + b^2 +2ab = (x+y)^2
or x+y = a+b
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Joined: 09 Sep 2013
Posts: 8821
Re: If x^2 + y^2 = 2ab and 2xy = a^2 + b^2, with a, b, x, y > 0, then x +  [#permalink]

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05 Sep 2018, 08:30
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Re: If x^2 + y^2 = 2ab and 2xy = a^2 + b^2, with a, b, x, y > 0, then x + &nbs [#permalink] 05 Sep 2018, 08:30
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