Question

if x= 1/√5-√3, then find the value x²- 1/x²​

Answer 1

Step-by-step explanation:

You square X and plug it into the formula given.

Perhaps this is complicated enough to be confusing… so let's do it one step at a time.

We know that we need x²… so let's find that first.

x = 2+ √3, so let's square that.

x² = (2+ √3)(2+ √3)

We remember the FOIL rule, right? First, Outside, Inside, Last. So:

x² = (2+ √3)(2+ √3) = (4 + 2√3 + 2√3 + 3) = 7 + 4√3

So now we know what x² is. Now we want to plug that into x² + 1/x².

Answer 2

x = √5 +2

To find :

x² + 1/ x²

Solution:

x = √5 +2

⇒1/x=1/√5 + 2

⇒1/x=1/√5 +2x √5-2/ √5-2

⇒1/x = √5-2/(√5)²-(2) ²

⇒1/x = √5-2/5-4

⇒1/x = √5-2

Now,

x+1/x = √5 + 2 + √5-2

x+1/x = 2√5

Again,

On squaring both sides, we have;

(x+1/x)² = (2√5)²

⇒ x² + 1/ x² + 2 = 20

⇒x²+1/x²= 20-2

⇒ x² + 1/ x² = 18

Hence,

The value of x² + 1/ x² = 18.

Step-by-step explanation:

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