Question

x - y = 4 ; 1/y - 1/x = 4/21 find x and y​

Answer 1

Answer:

Let two numbers be X and Y.

According to question,

Difference of two numbers =>4

X - Y = 4 --------(1)

Reciprocal of X is 1/X and Reciprocal of Y is 1/Y.

1/X - 1/Y = 4/21

Y - X / XY = 4/21

21(Y - X ) = 4XY

21Y - 21X = 4XY -------(2)

From equation (1) we get,

X - Y = 4

X = 4 + Y ------(3)

Putting the value of X in equation (2)

21Y - 21X = 4XY

21Y - 21 ( 4 + Y) = 4(4+Y) × Y

21Y - 84 - 21Y = (16 + 4Y)Y

-84 = 16Y + 4Y²

4Y² + 16Y + 84 = 0

4Y² + 28Y - 12Y + 84 = 0

4Y ( Y + 7 ) - 12 ( Y + 7) = 0

( Y + 7) ( 4Y - 12) = 0

(Y+7) = 0 OR (4Y-12) = 0

Y = -7 OR Y = 12/4 = 3

Putting Y = 3 in equation (3)

X = 4 +Y

X = 4+3 = 7

Hence,

Two numbers are 7 and 3.

Answer 2

Answer:

Thus, the two numbers are 7 and 3 respectively.

Step-by-step explanation:

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