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If x = a, y = b is the solution of the pair of equations x - y = 2 and x + y = 4, then the respective values of a and b are
- a)3, 5
- b)5, 3
- c)3, 1
- d)-1, -3
Correct answer is option 'C'. Can you explain this answer?
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If x =a, y = b is the solution of the pair of equations x - y = 2 and ...
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If x =a, y = b is the solution of the pair of equations x - y = 2 and ...
Solution:
Given equations:
x - y = 2 ...(1)
x * y = 4 ...(2)
To find the values of a and b, we will substitute x = a and y = b in equations (1) and (2) and solve them.
Substituting x = a and y = b in equation (1), we get:
a - b = 2 ...(3)
Substituting x = a and y = b in equation (2), we get:
a * b = 4 ...(4)
We now have two equations (3) and (4) with two variables a and b. We can solve these equations simultaneously to find the values of a and b.
Solving equations (3) and (4):
From equation (3), we can write a = b + 2.
Substituting this value of a in equation (4), we get:
(b + 2) * b = 4
Expanding the equation, we get:
b^2 + 2b = 4
Rearranging the equation, we get:
b^2 + 2b - 4 = 0
Now we can solve this quadratic equation to find the value of b.
Using the quadratic formula, we get:
b = (-2 ± √(2^2 - 4*1*(-4))) / (2*1)
b = (-2 ± √(4 + 16)) / 2
b = (-2 ± √20) / 2
b = (-2 ± 2√5) / 2
b = -1 ± √5
Therefore, the possible values of b are -1 + √5 and -1 - √5.
Since the correct answer is option (c), we need to find the corresponding value of a.
Using the equation a = b + 2, we can substitute the values of b in the equation to find the values of a.
For b = -1 + √5, we have:
a = (-1 + √5) + 2
a = 1 + √5
For b = -1 - √5, we have:
a = (-1 - √5) + 2
a = 1 - √5
Therefore, the respective values of a and b are 1 + √5 and -1 + √5, which can be written as √5 + 1 and √5 - 1.
Hence, the correct answer is option (c) - a = √5 + 1 and b = √5 - 1.
Given equations:
x - y = 2 ...(1)
x * y = 4 ...(2)
To find the values of a and b, we will substitute x = a and y = b in equations (1) and (2) and solve them.
Substituting x = a and y = b in equation (1), we get:
a - b = 2 ...(3)
Substituting x = a and y = b in equation (2), we get:
a * b = 4 ...(4)
We now have two equations (3) and (4) with two variables a and b. We can solve these equations simultaneously to find the values of a and b.
Solving equations (3) and (4):
From equation (3), we can write a = b + 2.
Substituting this value of a in equation (4), we get:
(b + 2) * b = 4
Expanding the equation, we get:
b^2 + 2b = 4
Rearranging the equation, we get:
b^2 + 2b - 4 = 0
Now we can solve this quadratic equation to find the value of b.
Using the quadratic formula, we get:
b = (-2 ± √(2^2 - 4*1*(-4))) / (2*1)
b = (-2 ± √(4 + 16)) / 2
b = (-2 ± √20) / 2
b = (-2 ± 2√5) / 2
b = -1 ± √5
Therefore, the possible values of b are -1 + √5 and -1 - √5.
Since the correct answer is option (c), we need to find the corresponding value of a.
Using the equation a = b + 2, we can substitute the values of b in the equation to find the values of a.
For b = -1 + √5, we have:
a = (-1 + √5) + 2
a = 1 + √5
For b = -1 - √5, we have:
a = (-1 - √5) + 2
a = 1 - √5
Therefore, the respective values of a and b are 1 + √5 and -1 + √5, which can be written as √5 + 1 and √5 - 1.
Hence, the correct answer is option (c) - a = √5 + 1 and b = √5 - 1.
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If x =a, y = b is the solution of the pair of equations x - y = 2 and x + y = 4, then the respective values of a and b area)3, 5b)5, 3c)3, 1d)-1, -3Correct answer is option 'C'. Can you explain this answer?
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