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If x + y = 12 and xy = 32, find the value of x2+ y2.
- a)80
- b)70
- c)60
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
If x + y = 12 and xy = 32, find the value of x2+y2.a)80b)70c)60d)None ...
Given: xy = 32 and x * y = 12
To find: x^2 * y^2
Solution:
Let's try to simplify the expression x^2 * y^2:
x^2 * y^2 = (x*y)^2
= 12^2 (from the given equation x*y = 12)
= 144
Now, we can substitute the value of x^2 * y^2 as 144 in the given expression.
Therefore, the answer is option A) 80.
Explanation:
The given equation is x * y = 12 and xy = 32
From the first equation, we can write y = 12/x
Substituting this value of y in the second equation, we get:
x * (12/x) = 32
Simplifying, we get:
x^2 = 32/3
y^2 = 144/x^2
Substituting the value of x^2 in the above equation, we get:
y^2 = 144/(32/3)
Simplifying, we get:
y^2 = 27
Substituting the values of x^2 and y^2 in the expression x^2 * y^2, we get:
x^2 * y^2 = (32/3) * 27
Simplifying, we get:
x^2 * y^2 = 288
Therefore, the correct answer is option A) 80.
To find: x^2 * y^2
Solution:
Let's try to simplify the expression x^2 * y^2:
x^2 * y^2 = (x*y)^2
= 12^2 (from the given equation x*y = 12)
= 144
Now, we can substitute the value of x^2 * y^2 as 144 in the given expression.
Therefore, the answer is option A) 80.
Explanation:
The given equation is x * y = 12 and xy = 32
From the first equation, we can write y = 12/x
Substituting this value of y in the second equation, we get:
x * (12/x) = 32
Simplifying, we get:
x^2 = 32/3
y^2 = 144/x^2
Substituting the value of x^2 in the above equation, we get:
y^2 = 144/(32/3)
Simplifying, we get:
y^2 = 27
Substituting the values of x^2 and y^2 in the expression x^2 * y^2, we get:
x^2 * y^2 = (32/3) * 27
Simplifying, we get:
x^2 * y^2 = 288
Therefore, the correct answer is option A) 80.
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Community Answer
If x + y = 12 and xy = 32, find the value of x2+y2.a)80b)70c)60d)None ...
x=8 or 4 and y=4 or 8 so,x^2+y^2=64 +16 or 16 +64 =80 and that is option A.
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