Question

If (x - y) = 13 and xy=-5, then find the value of 1/3(x2 + y2).​

Answer 1

Step-by-step explanation:

(x-y)=13

(x-y)^2=13^2

x^2 + y^2 - 2xy=169

now xy= -5

x^2+y^2 -2×(-5)=169

x^2+y^2+10=169

x^2 +y^2=169-10

x^2+y^2=159

now we know the value of x^2+y^2

so,1/3(x^2 +y^2)

=1/3(159) = 53 ans..

Answer 2

x-y=13
squaring on both sides
(x-y)^2=13^2
x^2+y^2-2xy=169
xy=-5
x^2+y^2-2(-5)=169
x^2+y^2+10=169
x^2+y^2=159
We need to find the value of 1/3(x^2+y^2)
Substituting the value of x^2+y^2
1/3(159)
=53
Therefor the value of 1/3(x^2+y^2)=53