Question

If x - y = 5 and xy = 24, find the value of (x + y).​

Answer 1

(x+y)² = x² + y² + 2xy

and

(x-y)² = x² +y² -2xy

now

(x+y)² - (x-y)² = 4xy

put the value of

x-y =5 and xy = 24

so now

(x+y)² - 5² = 4×24

(x+y)² = 96 +25

x+y = √121

x+y = 11

Answer 2

Answer:

(x+y) = ±11

Step-by-step explanation:

given,

x - y = 5 and xy = 24

x + y = ?

we can solve it in two ways either by using or identity or by finding values of x and y.

By using algebraic identity,

(x+y)² = (x-y)²+ 4xy

(x+y)² = (5)² + 4(24)

(x+y)² = 25 + 96

(x+y)² = 121

(x+y)² = 11²

(x+y) = ±11

By finding x and y,

=> x - y = 5

x = 5 + y

=> xy = 24

(5+y)(y) = 24

y² + 5y - 24 = 0

y² + 8y - 3y - 24 = 0

y (y+8) - 3(y+8) = 0

(y +8)(y-3) = 0

y = 3 (or) -8

=> If y = 3, then x = 5 + 3 = 8

  x + y = 8 + 3

           = 11

=> If y = -8,then x = 5 - 8 = -3

  x + y = -8-3

           =  -11

x + y = ±11

hope it helps..!