Question

if x+y=13 and xy= 25/4 find ( x-y)

Answer 1

Answer

Answr is in the attachment. Plz mrk it as brainliest

Answer 2

Hi

we have, x + y = 13. --------(1)
xy = 25/4 ---------(2)
we find, x - y = ?

squaring equation (1)

(x + y) ^2 =( 13)^2

using the identity
x2 + y2+ 2xy = 169

substituting the value of xy in the equation
x2 +y2 + 2* 25 / 4 = 169
x2 + y2 + 25/2 = 169
x2 + y2 + 12.5 = 169
x2 + y2 = 169 - 12.5
x2 + y2 = 156.5

now we have to find (x - y) , let us take x - y = a

squaring the equation

(x-y) ^2 = a ^2
x2 + y2 - 2xy = a2

substitute the value of xy

x2 + y2 -2* 25/4 = a2
x2 + y2 - 25/2 = a2
x2 + y2 -12.5 = a2

we find the value of x2 + y2
therefore put the value
156.5 - 12.5 = a2
144 = a2
a = √144
a = +12 , -12

therefore, x - y = +12 or -12

May it is helpful for you.