Question

If x=1/a + b

and y = 1/a-b
find the value of
х/y+ xy + x + y.
a) a2+ b2 - 2ab + 2a +1
a2 - b2
b) a2 + b² + 2ab – 2a +1
a2- b2
c) a2+ b2 - 2ab + 2a - 1
a2- b2
d) a2- b2- 2ab + 2a + 1
a2 - b2

Answer 1

Given :

• x = 1/a+b

• y = 1/a-b

To find

• x/y + xy + x + y

Solution :

• x/y

→ 1/a+b/1/a-b

→ 1/a+b × a-b

→ a-b/a+b

• xy

→ 1/a+b × 1/a-b

→ 1/a² - b²

• x + y

→ 1/a+b + 1/a - b

→ a - b + a + b/a² - b²

→ 2a/a² - b²

• Put the value of i, ii and iii

→ x/y + xy + x + y

→ a-b/a+b + 1/a² - b² + 2a/a² - b²

→ (a - b)(a-b) + 1 + 2a/a² - b²

→ (a - b)² + 1 + 2a/a² - b²

→ a² + b² - 2ab + 1 + 2a/a² - b²

• Option (a) is the correct one