Question

if x+ y= 13 and x-y = 13 and xy = 6¼ find x-y.​

Answer 1

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.

Answer 2

HEY MATE!!

X - Y = 12

OR - 12