Question

If 2(x-y)^2 = 116 and xy=24, find the value of x^2+ y^2

Answer 1

Answer:

106

Step-by-step explanation:

given:

2(x-y)^2=116, xy=24

to find:

x^2+y^2

solution:

2(x-y)^2=116

2(x^2-2xy+y^2)=116. .....[identity(a-b)=a^2-2ab+b^2]

2(x^2+y^2-2xy)=116

2(x^2+y^2-2(24))=116 .....as xy=24

2(x^2+y^2-48)=116

x^2+y^2-48=116/2

x^2+y^2-48=58

x^2+y^2=58+48

x^2+y^2=106