if x + y = 13 and xy =16 1/4 , find x - y
Answers
Answer:
We know that x+y=13 and xy= 25/4.
Squaring both sides of the first equation, we get-
(x+y)^2 = 13^2
x^2 + y^2 + 2xy = 169 (using the identity)
Putting in the value of xy, we get-
x^2+ y^2 + 25/2 = 169
x^2 + y^2 + 12.5 = 169
Subtracting 12.5 from both sides-
x^2 + y^2 = 156.5
Now, we have to find (x-y). Let x-y be equal to ‘a’.
x-y = a
(x-y)^2 = a^2
x^2 + y^2 - 2xy = a^2
Putting in the values of x^2+y^2 and xy, we get-
156.5 - 2*25/4 = a^2
156.5 - 25/2 = a^2
156.5 - 12.5 = a^2
144 = a^2
Taking the square root of both sides,
a = +- 12 (either 12 or - 12)
Hence, x-y = 12 or -12.
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