Question

( x – y ) = 6 and xy = 16 then ( x + y ) = ? a) 100 b)10 c) 22 d) 4 hint : [ (x + y ) = √(x − y) 2 + 4xy]

Answer 1

b

Explanation:

(x - y)² = x² - 2xy + y² → (1)

(x + y)² = x² + 2xy + y² → (2)

Subtract (1) from (2)

(x + y)² - (x - y)² = 2xy - (- 2xy) = 2xy + 2xy = 4xy

Add (x - y)² to both sides

(x + y)² = (x - y)² + 4xy ( take the square root of both sides )

x + y =
`√((x-y)^2+4xy)`, that is

x + y =
`√(6^2+4(16))` =
`√(36+64)` =
`√(100)` = 10 → b

Answer 2

10

Take x as 8 and y as 2
Then, 8 - 2 = 6
8 x 2 = 16
So 8 +2=10