If x

Question

If  x < y , and  y(y − 2x) =2 − x^2 , what is the value of  x − y ?

(A)  −2 
 
(B)  −\sqrt{2} 
 
(C)  −1 
 
(D)  1 
 
(E)  \sqrt{2}

Bunuel · Accepted Answer

y(y-2x)=2- x^2 ;

y^2-2xy=2-x^2 ;

y^2-2xy+x^2=2 ;

(x-y)^2=2 .

Since x<y (x-y<0), then  x-y=-\sqrt{2} .

Answer: B.

Hope it's clear.

livfcind · Answer

Explanation:   y(y-2x)=2 - x^2

y^2 - 2xy=2 - x^2

x^2 + y^2 -2xy=2

(x-y)^2 = 2,

x-y = -\sqrt{2}  (given x<y ,thus x-y <0)

Hence B is the correct answer.

chetan2u · Answer

x<y or x-y<0, so our answer has to be negative. You can eliminate the positive values.

y(y − 2x) =2 − x^2

y^2− 2xy=2 − x^2

x^2-2xy+y^2=2

(x-y)^2=2

x-y=\sqrt{2}=-\sqrt{2}

But x-y<0, so answer is B

Showmeyaa · Answer

y(y − 2x) =2 − x^2 
 y^2 - 2xy = 2 - x^2 
 x^2 - y^2 -2xy = 2 
 (x-y)^2 = 2 
Taking square roots both sides
 |x-y| = \sqrt{2} 
 x - y = -\sqrt{2}  (As, y < x)

Kinshook · Answer

Asked: If  x < y , and  y(y − 2x) =2 − x^2 , what is the value of  x − y ?

y(y − 2x) =2 − x^2 
 y^2 - 2xy =2 − x^2 
 x^2 + y^2 - 2xy =2 
 (x-y)^2 =2 
 x-y =-\sqrt{2} ; since x<y

IMO B

shikha_0203 · Answer

Why are we taking the answer as - sqrt 2. It could also be +ve. Please help me know the reason behind it.

Bunuel · Answer

This is explained. You just have to read the solutions carefully:

(x-y)^2=2 .

Since x < y (x - y < 0), then  x-y=-\sqrt{2} .

bumpbot · Answer

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If x < y, and y(y − 2x) = 2 − x^2, what is the value of x − y?

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