Question

1/x - 1/y = 1/4 1/x^2 - 1/y^2 = 3/16 x + y = ...

Answer 1

GIVEN:

• 1/x - 1/y = ¼.
• 1/x² - 1/y² = 3/16.

TO FIND:

• The value of x + y.

ANSWER:

Firstly let us assume ,

• p = 1/x .
• q = 1/y .

Now the equⁿ s becomes ,

=> p - q = 4 . ........(1)

Also , given that:

=> 1/x² - 1/y² = 3/16.

=> p² - q² = 3/16.

=> (p+q)(p-q) = 3/16.

From (1),

=> 4 (p+q) = 13/16.

=> (p+q) = 13/16 × 1/4.

=> p+ q = 13/64.

On adding (1) and (2) ,

=> 2p = 4 + 13/64.

=> 2p = 256+13/64.

=> p = 269/64 × 1/2.

=> p = 269/128.

Now lets find q ,

=> q = 13/64 - 269/128.

=> q = 26-269/128.

=> q = -243/128.

Hence

• p = 269/128.
• q = -243/128.

.°. x = 128/269 , y = -128/243