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# What is the value of x^2 + y^2 ?

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Math Expert
Joined: 02 Sep 2009
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What is the value of x^2 + y^2 ?  [#permalink]

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11 Nov 2019, 04:48
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Difficulty:

55% (hard)

Question Stats:

56% (01:47) correct 44% (01:55) wrong based on 34 sessions

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What is the value of $$x^2 + y^2$$ ?

(1) $$x^2 + y^2 = 2xy + 1$$

(2) $$x^2 + y^2 = 4 -2xy$$

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Re: What is the value of x^2 + y^2 ?  [#permalink]

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11 Nov 2019, 07:52
What is the value of $$x^2 + y^2$$ ?

(1) $$x^2 + y^2 = 2xy + 1$$
if x=y=1, $$x^2 + y^2 = 2xy + 1=2*1*1+1=3$$
if x=y=0, $$x^2 + y^2 = 2xy + 1=2*0*0+1=1$$
Insuff

(2) $$x^2 + y^2 = 4 -2xy$$
if x=y=1, $$x^2 + y^2 = 4-2xy =4-2*1*1=2$$
if x=y=0, $$x^2 + y^2 = 4-2xy =4-2*0*0=4$$
Insuff

Combined...
$$x^2 + y^2+ x^2 + y^2 = 4 -2xy+ 2xy + 1......2(x^2+y^2)=5.....x^2+y^2=\frac{5}{2}$$
Suff

C
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Re: What is the value of x^2 + y^2 ?  [#permalink]

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12 Nov 2019, 09:44
Option c makes the catch as we can only find with these two equations

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Re: What is the value of x^2 + y^2 ?   [#permalink] 12 Nov 2019, 09:44
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