Question

. If x² + y² = 29 and xy = 2. find the values of
(ii) x + y
(1) X - y​

Answer 1

Firstly:-

We know that (a+b)^2 = a^2+ b^2 + 2ab

Now applying in the equations for getting the required solution.

First:- (x+y)

(x+y)^2= x^2 + y^2 + 2xy
(X+y)^2 = 29 + 2(2) [ as x^2 + y^2 =
29, xy=2]
(X+y)^2 = 29+ 4
(X+y)^2 = 33
Therefore x+y = root of 33.

Similarly for (x-y)

(X-y)^2 = x^2 + y^2 - 2xy
(X-y)^2 = 29 - 2(2)
(X-y)^2 = 29 -4
(X-y)^2 = 25
Therefore, x-y = 5 [ as the root of
25 is 5 ]