Question : If $x^{2} + y^{2} + 2 y + 4 x + 5 = 0$ , then $\frac{x + y}{x - y} =$ ______.
Option 1: $- 3$
Option 2: $\frac{1}{3}$
Option 3: $- 1$
Option 4: $3$

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Question : If $x^{4} + y^{4} + x^{2} y^{2} = 17 \frac{1}{16}$ and $x^{2} - x y + y^{2} = 5 \frac{1}{4}$ , then one of the values of $(x - y)$ is:

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Answer 1

Correct Answer: $3$

Solution : Given equation, $x^{2} + y^{2} + 2 y + 4 x + 5 = 0$
Let us try to make it a perfect square.
$x^{2} + 4 x + y^{2} + 2 y + 5 = 0$
⇒ $x^{2} + 4 x + 4 - 4 + y^{2} + 2 y + 1 - 1 + 5 = 0$
⇒ $(x + 2)^{2} + (y + 1)^{2} - 5 + 5 = 0$
⇒ $(x + 2)^{2} + (y + 1)^{2} = 0$
⇒ $(x + 2)^{2} = 0$ and $(y + 1)^{2} = 0$ [If the sum of two squares is zero then each term individually will also be zero]
⇒ $x + 2 = 0$ and $y + 1 = 0$
⇒ $x = - 2$ and $y = - 1$
$∴$ $\frac{x + y}{x - y} = \frac{- 2 - 1}{- 2 + 1} = \frac{- 3}{- 1} = 3$
Hence, the correct answer is 3.

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Question : If x2+y2+2y+4x+5=0, then x+yx−y=______.Option 1: −3Option 2: 13Option 3: −1Option 4: 3

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Question : If $x^{2} + y^{2} + 2 y + 4 x + 5 = 0$ , then $\frac{x + y}{x - y} =$ ______.
Option 1: $- 3$
Option 2: $\frac{1}{3}$
Option 3: $- 1$
Option 4: $3$