Question

if x= 2-\sqrt{3} . fin value of x^{2} +1/x^{2} and x^{2} -1/x^{2}

Answer 1

Answer:

a)=6/7 b=8/7

Step-by-step explanation:

x^2=(2-root3)^2

x^2=4root3-7.....(put on 1 equatio)

we get:4root3-7 +1/4root3-7

4root3 se 4root3 cancle

so we get

Answer 2

Question :

If x = 2 - √3 . Find the value of x² + 1/x² and x² - 1/x² ?

ANSWER

Given : -

x = 2 - √3

Required to find : -

• value of x² + 1/x² ?

• value of x² - 1/x² ?

Solution : -

x = 2 - √3

we need to find the values of x² + 1/x² and x² - 1/x² ?

So,

Firstly ,

Let's find the value of x² !

➜ x = 2 - √3

➜ 2 - √3

➜ ( 2 - √3 )²

Using the Identity ;

• ( a - b )² = a² + b² - 2ab

➜ ( 2 - √3 )² =

➜ ( 2 )² + ( √3 )² - 2 ( 2 ) ( √3 )

➜ 4 + 3 - 4 ( √3 )

➜ 7 - 4√3

Hence,

• value of x² = 7 - 4√3

Now,

Let's find the value of x² + 1/x²

➜ x² + 1/x²

Here,

➜ 1/x² =

➜ 1/7 - 4√3

Multiply the numerator and denominator with 7 + 4√3

➜ 1/7 - 4√3 x 7+4√3/7+4√3

Using the identity ;

• ( a + b ) ( a - b ) = a² - b²

➜ 7+4√3/ ( 7 )² - ( 4√3 )²

➜ 7+4√3/49 - 16 x 3

➜ 7+4√3/49 - 48

➜ 7+4√3/1

➜ 7+4√3

This implies ;

value of x² = 7 - 4√3

value of 1/x² = 7 + 4√3

So,

Value of x² + 1/x is ;

➜ 7 - 4√3 + 7 + 4√3

➜ - 4√3 , + 4√3 gets cancelled

➜ 7 + 7

➜ 14

Similarly,

Value of x² - 1/x²

➜ 7 - 4√3 - ( 7 - 4√3 )

➜ 7 - 4√3 - 7 + 4√3

➜ All the terms get cancelled due to their alternative signs

➜ 0

Therefore,

Value of x² + 1/x² = 14 ↤

Value of x² - 1/x² = 0 ↤

- : Additional Information : -

Question

What is Rationalising ?

Answer

Rationalising is a process by which we can eliminate the denominator of any algebraic expressions .

This process involves by multiplying the expression with the same one but with an alternative sign.

For example : -

Rationalising factor of 5 + 3√2 is 5 - 3√2 .

Rationalising factor of 1 - 2 √5 is 1 + 2√15 .

Similarly,

Rationalising factor of √5 is √5 .

This method works for both complex number system and real numbers also .

By rationalising we can expand the denominator if required and also we can reduce the size of a denominator too .

With these we also use some algebraic Identities they are ;

• ( x + y ) ( x - y ) = x² - y²

• ( x + a ) ( x + b ) = x² + x ( a + b ) + ab

• ( x + y )² = x² + y² + 2xy

• ( x - y )² = x² + y² - 2xy