Question

given that x^2 + y^2 = 193 and xy = 84, find the value of x + y and x - y.

Answer 1

★ Given :

x² + y² = 193

xy = 84

★ To find:

value of x+y and x-y

★ Solution:

We know that,

${\pink{\boxed{(a+b)^2 = a^2 + b^2 + 2ab}}}$

${\pink{\boxed{(a-b)^2 = a^2 + b^2 - 2ab}}}$

by putting the values

(x+y)² = x² + y² + 2xy

(x+y)² = 193 + 2(84)

= 193+168

= 361

(x+y)² = 361

(x+y) = √361

→ (x+y) = 19

(x-y)² = x² + y² -2xy

= 193 - 2(84)

= 193 - 168

= 25

(x-y)² = 25

(x-y) = √25

→ (x-y) = 5