If x + y = 27 and $x^2 + y^2 = 425, $ then the value of $(x-y)^2$ will be :
Answer & explanation
Correct answer: option 3
We know that,
(x + y)2 = x2 + y2 + 2xy
(x – y)2 = x2 + y2 – 2xy
Given,
x + y = 27
x2 + y2 = 425
(x + y)2 = x2 + y2 + 2xy
= (27)2 = 425 + 2xy
= 729 = 425 + 2xy
= 2xy = 729 – 425
= 2xy = 304
Also,
(x – y)2 = x2 + y2 – 2xy
= (x – y)2 = 425 – 304
= (x – y)2 = 121