If x/y+y/x=4, find the value of x/y-y/x
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Step-by-step explanation:
By using Formula
(x/y-y/x)^2 = x^2/y^2 + y^2/x^2 - 2(x/y)(y/x)
(x/y-y/x)^2 = x^2/y^2 + y^2/x^2 - 2
(x/y-y/x)^2 = (x/y+y/x)^2 - 2(x/y)(y/x) - 2
(x/y-y/x)^2 = (x/y+y/x)^2 - 2 - 2
(x/y-y/x)^2 = (4)^2 - 2 - 2
(x/y-y/x)^2 = 16 - 4
(x/y-y/x)^2 = 12
Taking square root on both side
(x/y - y/x)= sqrt ( 12 )
Answer:
x ^ y = y ^ x
or x = y ^ (x / y)
or y = y ^ (y / x)
x/y = (y ^ (x / y))/y = y ^ ((x / y) - 1) = (x ^ (x / y)) ^ [(x / y) - 1]
or (x/y) ^ (x / y) = \{x ^ (x / y * [(x / y) - 1])\} ^ (x / y) = x ^ ((x / y) - 1)
Step-by-step explanation:
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