If x= 8+3√7 and xy =1 , Then value of x+y ?
Question
If x= 8+3√7 and xy =1 , Then value of x+y ?
Solution
To solve this problem, we need to find the value of y first.
Given that xy = 1, we can solve for y by dividing both sides of the equation by x:
y = 1/x
Substitute x = 8 + 3√7 into the equation:
y = 1/(8 + 3√7)
To rationalize the denominator, multiply the numerator and the denominator by the conjugate of the denominator, which is (8 - 3√7):
y = (1*(8 - 3√7))/((8 + 3√7)*(8 - 3√7))
Simplify the denominator using the difference of squares formula (a^2 - b^2 = (a - b)(a + b)):
y = (8 - 3√7)/(8^2 - (3√7)^2)
Simplify further:
y = (8 - 3√7)/(64 - 63)
y = 8 - 3√7
Now that we have the values of x and y, we can find the value of x + y:
x + y = (8 + 3√7) + (8 - 3√7)
x + y = 16
So, the value of x + y is 16.
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