Question

y= 5+√3 , y+1/y = ?
Plese do this step by step​

Answer 1

Answer:

y + 1/y = (27 - √3)/22

Step-by-step explanation:

y + 1/y = (5 + √3 + 1) / (5 + √3)

=> (6 + √3)/(5 + √3)

By rationalizing the denominator,

=> (6 + √3) (5 - √3) / (5 + √3) (5 - √3)

=> (6 x 5) - (6 x √3) + (√3 x  5) - (√3 x √3) / 5² - (√3)²

=> 30 - 6√3 + 5√3 - 3 / 25 - 3

=> (27 - √3) / 22

Answer 2

Refer to the attachment..

Steps that will help you to follow and find solution of any kind of such problems.

1. If y is a irrational number, then y is also a irrational number. Rationalize y such that the denominator becomes a rational number.
2. Now, rationalize means to multiply a irrational number to the given irrational number to make it a rational number. Like (3+√2)(3-√2) = 9 - 2 = 7
3. To do so, you need to know the algebraic identity (a + b)(a - b) = a² - b²
4. Now take the LCM
5. Compute the numerator and you will get the final answer.

Final answer of this Q.

$\large{ \boxed{ \boxed{ \tt{ \frac{115 + 21 \sqrt{3} }{22} }}}}$