Answer:
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15
x = √3 +1 / √3 -1 , y = √3 -1 / √3 +1
find x^2 + y^2 + xy
To solve this problem, we can simplify x and y first, then substitute them into the expression of x^2 + y^2 + xy.
Starting with x:
x = (√3 +1) / (√3 -1)
Rationalizing the denominator, we get:
x = [(√3 +1) / (√3 -1)] * [(√3 +1) / (√3 +1)]
x = (3 + 2√3 + 1) / (3 - 1)
x = 2 + √3
Now let's simplify y:
y = (√3 -1) / (√3 +1)
Again, rationalizing the denominator, we get:
y = [(√3 -1) / (√3 +1)] * [(√3 -1) / (√3 -1)]
y = (3 - 2√3 + 1) / (3 - 1)
y = 2 - √3
Now we can substitute these values into the expression of x^2 + y^2 + xy:
x^2 + y^2 + xy = (2 + √3)^2 + (2 - √3)^2 + (2 + √3)(2 - √3)
= 4 + 3 + 4√3 + 4 + 3 - 4√3+1
= 15
Therefore, x^2 + y^2 + xy = 15
Thanks
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Answer:
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Step-by-step explanation:
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Verified answer
Answer:
15
Step-by-step explanation:
x = √3 +1 / √3 -1 , y = √3 -1 / √3 +1
find x^2 + y^2 + xy
To solve this problem, we can simplify x and y first, then substitute them into the expression of x^2 + y^2 + xy.
Starting with x:
x = (√3 +1) / (√3 -1)
Rationalizing the denominator, we get:
x = [(√3 +1) / (√3 -1)] * [(√3 +1) / (√3 +1)]
x = (3 + 2√3 + 1) / (3 - 1)
x = 2 + √3
Now let's simplify y:
y = (√3 -1) / (√3 +1)
Again, rationalizing the denominator, we get:
y = [(√3 -1) / (√3 +1)] * [(√3 -1) / (√3 -1)]
y = (3 - 2√3 + 1) / (3 - 1)
y = 2 - √3
Now we can substitute these values into the expression of x^2 + y^2 + xy:
x^2 + y^2 + xy = (2 + √3)^2 + (2 - √3)^2 + (2 + √3)(2 - √3)
= 4 + 3 + 4√3 + 4 + 3 - 4√3+1
= 15
Therefore, x^2 + y^2 + xy = 15
Thanks