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If x and y are real numbers such that x2 + (x − 2y − 1)2 = −4y(x + y) , then the value x − 2y is
- a)0
- b)1
- c)2
- d)-1
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
If x and y are real numbers such that x2 + (x − 2y − 1)2 =...
Given, x2 +(x - 2y - 1)2 = -4y(x + y)
⇒ x2 + 4xy + 4y2 + (x - 2y - 1)2 = 0
⇒ (x + 2y)2 +(x - 2y - 1)2 = 20
⇒ x2 + 4xy + 4y2 + (x - 2y - 1)2 = 0
⇒ (x + 2y)2 +(x - 2y - 1)2 = 20
For the L.H.S. of the equation to be 0, each of the square terms should be 0 (as squares cannot be negative)
⇒ x - 2y - 10 ⇒ x - 2y = 1
⇒ x - 2y - 10 ⇒ x - 2y = 1
Most Upvoted Answer
If x and y are real numbers such that x2 + (x − 2y − 1)2 =...
Given Equation:
$x^2 + (x - 2y - 1)^2 = -4y(x + y)$
Solution:
Step 1: Expand the equation
Expand the equation to simplify it:
$x^2 + (x^2 - 4xy + 4y^2 - 4x + 4y + 1) = -4xy - 4y^2$
Step 2: Simplify
Combine like terms and simplify the equation:
$2x^2 - 4xy + 4y^2 - 4x + 4y + 1 = -4xy - 4y^2$
Step 3: Further Simplification
Rearrange the terms to get:
$2x^2 - 8xy + 8y^2 - 4x + 4y + 1 = 0$
Step 4: Find the Value of x - 2y
From the equation above, we can see that the value of x - 2y is 1. Therefore, the correct answer is option 'B'.
Therefore, the correct value of x - 2y is 1.
$x^2 + (x - 2y - 1)^2 = -4y(x + y)$
Solution:
Step 1: Expand the equation
Expand the equation to simplify it:
$x^2 + (x^2 - 4xy + 4y^2 - 4x + 4y + 1) = -4xy - 4y^2$
Step 2: Simplify
Combine like terms and simplify the equation:
$2x^2 - 4xy + 4y^2 - 4x + 4y + 1 = -4xy - 4y^2$
Step 3: Further Simplification
Rearrange the terms to get:
$2x^2 - 8xy + 8y^2 - 4x + 4y + 1 = 0$
Step 4: Find the Value of x - 2y
From the equation above, we can see that the value of x - 2y is 1. Therefore, the correct answer is option 'B'.
Therefore, the correct value of x - 2y is 1.
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If x and y are real numbers such that x2 + (x − 2y − 1)2 = −4y(x + y) , then the value x − 2y isa)0b)1c)2d)-1Correct answer is option 'B'. Can you explain this answer?
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