Question

If
x =1/3+2√2,then the value of
x-1/x is​

Answer 1

Answer:

the answer to this question is given in the above attachment.

Answer 2

GIVEN :-

x = 1/(3 + 2√2) .

TO FIND :-

The value of x - 1/x.

SOLUTION :-

⇒ x = 1/(3 + 2√2)

By rationalizing the denominator we get,

⇒ x = {1 × (3 - 2√2)}/{(3 + 2√2)(3 - 2√2)}

By using identity :- (a + b)(a - b) = a² - b².

⇒ x = {(3 - 2√2)}/{(3)² - (2√2)²}

⇒ x = {(3 - 2√2)}/{9 - 4 × 2}

⇒ x = {(3 - 2√2)}/{9 - 8}

⇒ x = {(3 - 2√2)}/1

Hence we got the value of x = 3 - 2√2.

Now by using the above value of x we will find the value of x - 1/x.

⇒ x - 1/x.

Put the value of x = 3 - 2√2.

⇒ x - 1/x = (3 - 2√2) - 1/(3 - 2√2)

Taking LCM as 3 - 2√2 We get,

⇒ x - 1/x = {(3 - 2√2)(3 - 2√2) - 1}/{3 - 2√2}

⇒ x - 1/x = {(3 - 2√2)² - 1}/{3 - 2√2}

By using identity :- (a - b)² = a² + b² - 2ab.

⇒ x - 1/x = [{(3)² + (2√2) -2 × 3 × 2√2} - 1]/{3 - 2√2}

⇒ x - 1/x = (9 + 8 - 12√2 - 1)/(3 - 2√2)

⇒ x - 1/x = (16 - 12√2)/(3 - 2√2)

Again rationalizing the denominator we get,

⇒ x - 1/x = {(16 - 12√2)(3 - 2√2)}/{(3 - 2√2)(3 + 2√2)}

⇒ x - 1/x = {16(3 + 2√2) - 12√2(3 + 2√2)}/{(3)² - (2√2)²}

⇒ x - 1/x = (48 + 32√2 - 36√2 - 48)/(9 - 8)

⇒ x - 1/x = (32√2 - 36√2)/1

⇒ x - 1/x = -4√2.

Hence required value of x - 1/x = -4√2.