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DIRECTIONS for the question: Solve the following question and mark the best possible option.
Q. How many pairs of real numbers (x, y) satisfy the equation (x + y)2 = (x + 3) (y – 3) ?
- a)0
- b)1
- c)2
- d)Infinitely many
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
DIRECTIONSfor the question:Solve the following question and mark the b...
Let X = x + 3 and Y = y –3.
Then the given equation becomes (X + Y)2 = XY.
So X2 + XY + Y2 = 0.
X2 and Y2 are always non-negative.
Then the given equation becomes (X + Y)2 = XY.
So X2 + XY + Y2 = 0.
X2 and Y2 are always non-negative.
Let us take the scenario where XY is negative, which means (X + Y)2 = XY is negative, which is not possible.
Hence XY is also non negative.
Hence XY is also non negative.
We can conclude now, that X2, Y2 and XY are non-negative as well as non-positive, which means that both are equal to 0.
So x = – 3 and y = 3 is the only solution. Thus there is only one solution.
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DIRECTIONSfor the question:Solve the following question and mark the best possible option.Q. How many pairs of real numbers (x, y) satisfy the equation (x + y)2= (x + 3) (y – 3) ?a)0b)1c)2d)Infinitely manyCorrect answer is option 'B'. Can you explain this answer?
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