Question

if y equal to 2 plus root 3 find the value of y plus 1/y and y square plus 1 /y square​

Answer 1

$\huge\boxed{Answer}$

Given :-

y = 2 + √3

Have To Find Out :-

Value of (y + 1/y) & (y² + 1/y²)

Using Property :-

a² + 1/a² = (a + 1/a)² - 2

Explanation :-

=> y + 1/y

=> (2 + √3) + 1/(2 + √3)

=> {(2 + √3)² + 1 } / (2 + √3)

=> {4 + 3 + 4√3 + 1}/ (2 + √3)

=> (8 + 4√3) / (2 + √3)

=> 4(2 + √3) / (2 + √3)

=> 4

y + 1/y = 4

Now ,

y² + 1/y² = (y + 1/y)² - 2

= (4)² - 2

= 16 - 2

= 14

Result :-

(1) (y + 1/y) = 4

(2) (y² + 1/y²) = 14

Answer 2

Given:

y = 2 + √3

To Find:

The value of (y + 1/y) & (y² + 1/y²)

Solution:

By using the identity,

a² + 1/a² = (a + 1/a)² - 2.

Firstly, y + 1/y,

putting value of y in the above expression,

= (2 + √3) + 1/(2 + √3)

= {(2 + √3)² + 1 } / (2 + √3)

= {4 + 3 + 4√3 + 1}/ (2 + √3)

= (8 + 4√3) / (2 + √3)

= 4(2 + √3) / (2 + √3)

= 4

So, y + 1/y = 4

Now ,

y² + 1/y²

= (y + 1/y)² - 2

= (4)² - 2

= 16 - 2

= 14

So, (y² + 1/y²) = 14

Hence, the value of (y + 1/y) is 4 and the value of (y² + 1/y²) is 14.