Question

if x=√6+√5,then x2+1/x2-2=​

Answer 1

Answer:

20

Step-by-step explanation:

Given : If x = √6 + √5

To find : the value of : x² + 1/x² - 2

We have x = √6 + √5 …...…..(1)

∴ 1/x = 1/(√6 + √5)

By Rationalizing denominator, we have :

= 1 × (√6 -√5) / [(√6 + √5) × (√6 - √5)]

= (√6 - √5) / (√6)² - (√5)²

[We know that, (a + b) (a - b) = a² - b²]

= (√6 - √5)/(6 - 5)

= (√6 - √5 )/1

= √6 - √5

1/x = √6 - √5 ………(2)

Then, x² + 1/x² - 2

We know that, x² + 1/x² - 2 = (x - 1/x)²

On putting the value from eq 1 & 2 :

x² + 1/x² - 2 = [√6 + √5 - (√6 - √5 )]²

x² + 1/x² - 2 = [√6 + √5 - √6 + √5 ]²

x² + 1/x² - 2 = (√5 + √5)²

x² + 1/x² - 2 = (2√5)²

x² + 1/x² - 2 = 4 × 5

x² + 1/x² - 2 = 20

Hence, x² + 1/x² - 2 is 20.

Answer 2

Answer:

it's answer

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