Question

Maths expansion please solve qno. 9​

Answer 1

Answer:

0

Step-by-step explanation:

x=1/x-5 then dx/dy= 0/1-0  then 1.dx=0.dy then x.dx = 1 then x= 1

so now x²-1/x²  and x=1   then  1-1/1 ⇒0

Answer 2

Question:

If x = 1/(x-5) and x ≠ 5 , find : x^2 - 1/x^2.

Answer:

x^2 - 1/x^2 = 5√29

Note:

• (a+b)^2 = a^2 + b^2 + 2•a•b

• (a-b)^2 = a^2 + b^2 - 2•a•b

• a^2 - b^2 = (a-b)•(a+b)

• (a+b)^2 = (a-b)^2 + 4•a•b

• (a-b)^2 = (a+b)^2 - 4•a•b

Solution:

Given:

x = 1/(x-5)

To find:

x^2 - 1/x^2 = ?

We have,

=> x = 1/(x-5)

=> x•(x-5) = 1

=> x^2 - 5x = 1

=> x^2 - 1 = 5x

=> (x^2 - 1)/x = 5

=> (x^2)/x - 1/x = 5

=> x - 1/x = 5 --------(1)

Now,

We know that ;

(a+b)^2 = (a-b)^2 + 4•a•b

Thus;

=> (x + 1/x)^2 = (x - 1/x)^2 + 4•x•(1/x)

=> (x + 1/x)^2 = 5^2 + 4 {using eq-(1)}

=> (x + 1/x)^2 = 25 + 4

=> (x + 1/x)^2 = 29

=> x + 1/x = √29 ---------(2)

Also,

We know that;

a^2 - b^2 = (a-b)•(a+b)

Thus;

=> x^2 - 1/x^2 = (x - 1/x)•(x + 1/x)

{using eq-(1) and (2)}

=> x^2 - 1/x^2 = 5•√29

=> x^2 - 1/x^2 = 5√29

Hence,

The required value of x^2 - 1/x^2 is 5√29.