Question

Hey 40 marks challenge + brainliest.....





any math expert... plz tell where is my error or mistake...
i dont want answer just tell me where is my mistake
answer of this question is 7 and 3 or -7 and -3 but mine is not coming out....​

Answer 1

Question:

The difference between two numbers is 4. If the difference of their reciprocal is 4/21. Find the numbers.

Solution:

• Let one number be x and another number be y.

» Difference between two numbers is 4.

A.T.Q.

→ x - y = 4

→ y = 4 + x ________ (eq 1)

_____________________________

» The difference of their (let numbers) reciprocal is 4/21.

A.T.Q.

→ $\dfrac{1}{x}\:-\:\dfrac{1}{y}\:=\:\dfrac{4}{21}$

Take LCM

→ $\dfrac{y\:-\:x}{yx}\:=\:\dfrac{4}{21}$

Cross-multiply them

→ 21(y - x) = 4(xy)

→ 21y - 21x = 4xy

→ 21(4 + x) - 21x = 4x(4 + x)

→ 84 + 21x - 21x = 16x + 4x²

→ 84 = 16x + 4x²

→ 4x² + 16x - 84 = 0

→ 2x² + 8x - 42 = 0

→ x² + 4x - 21 = 0

→ x² + 7x - 3x - 21 = 0

→ x(x + 7) -3(x + 7) = 0

→ (x - 3) (x + 7) = 0

→ x = +3, -7

___________________________

Put value of of x in (eq 1)

If x = +3

→ y = 4 + 3

→ y = 7

If x = -7

→ y = 4 - 7

→ y = - 3

___________________________

One number = +3, -7 and another number is +7, -3.

________ [ ANSWER ]

___________________________

☞ Your mistake:

You let first number x and another y. But in 2nd case, you put the another number i.e. y before x.

=> 1/y - 1/x = 4/21 (It's wrong)

The correct one is

=> 1/x - 1/y = 4/21

____________________________

Answer 2

your mistake is ....

in first condition u took......X>y

i.e..x-y=4

but ... remember if X>y then

$\frac{1}{x} < \frac{1}{y}$

so when u are taking...X-y=4 [X>y]

then its corresponding part should ..be..

$\frac{1}{y} - \frac{1}{x} = \frac{4}{21}$

but u took...X-y=4. and (1/X)-(1/y)=4/21

and this is wrong.......