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wlad13 [49]
3 years ago
14

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

Mathematics
1 answer:
Nostrana [21]3 years ago
6 0

<u>GIVEN</u><u>:</u>

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

<u>TO</u><u> </u><u>FIND</u><u>:</u>

  • The value of x + y.

<u>ANSWER</u><u>:</u>

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.

<u>He</u><u>nce</u><u> </u>

  • <u>p</u><u> </u><u>=</u><u> </u><u>2</u><u>6</u><u>9</u><u>/</u><u>1</u><u>2</u><u>8</u><u>.</u>
  • <u>q</u><u> </u><u>=</u><u> </u><u>-</u><u>2</u><u>4</u><u>3</u><u>/</u><u>1</u><u>2</u><u>8</u><u>.</u>

.°. x = 128/269 , y = -128/243

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