Question

tell this..............

Answer 1

Answer:

7,3 (or) -3,-7

Step-by-step explanation:

Let the numbers be a and b. {Let a > b}

Now,

a - b = 4   ---- (i)

(1/b) - (1/a) = (4/21)  

⇒ (a - b)/ab = 4/21

⇒ (a - b) = 4ab/21

⇒ 4 = 4ab/21

⇒ 84 = 4ab

⇒ ab = 21.

⇒ a = (21/b)   ---- (ii)

Substitute (ii) in (i), we get

⇒ (21/b) - b = 4

⇒ 21 - b² = 4b

⇒ b² + 4b - 21 = 0

⇒ b² + 7b - 3b - 21 = 0

⇒ b(b + 7) - 3(b + 7) = 0

⇒ b = 3,-7

When b = 3:

a - b = 4

a - 3 = 4

a = 7

When b = -7:

a - b = 4

a + 7 = 4

a = -3

Therefore, the numbers are : 7,3 (or) -3,-7.

Hope it helps!

Answer 2

Let the numbers be a and b

b - a = 4 ...............................(1)

Difference of reciprocal = 4/21

==> 1/a - 1/b = 4/21

==> ( b - a ) / ab = 4/21

==>  4 / ab = 4 / 21 [ From ( 1 )]

==> 1/ab = 1/21

==> ab = 21

==> a = 21/b ......................(2)

Now putting this value in (1) we get :

b - 21/b = 4

==> ( b² - 21) / b = 4

==> b² -21 = 4b

==> b² - 4b - 21 = 0

==> b² - 7b + 3b -21 = 0

==> b ( b - 7 ) + 3 ( b - 7 ) = 0

==> ( b -7 )( b + 3 ) = 0

Either b = 7 or , b = -3

Either

b - a = 4

==> 7 - a = 4

==> a = 3

or ,

b - a = 4

==> -3 - a = 4

==> -a = 4 + 3

==> a = -7

The values are as follows :

Numbers can be 7 and 3 or -7 and -3

#JISHNU#

Hope it helps ^_^

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