Question

if x is equal to 3 + root 8 then find the value of x square + 1 / x square​

Answer 1

Step-by-step explanation:

hope you all understand

Answer 2

Step-by-step explanation:

Given :-

x = 3+√8

To find :-

Find the value of x²+(1/x²) ?

Solution :-

Given that :

x = 3+√8 --------------(1)

=> 1/x = 1/(3+√8)

The denominator = 3+√8

The Rationalising factor of 3+√8 is 3-√8

On Rationalising the denominator then

=> 1/x = [1/(3+√8)]×[(3-√8)/(3-√8)]

=> 1/x =(3-√8)/[(3+√8)(3-√8)]

=> 1/x = (3-√8)/[3²-(√8)²]

Since (a+b)(a-b) = a²-b²

Where , a = 3 and b = √8

=> 1/x = (3-√8)/(9-8)

=> 1/x = (3-√8)/1

=> 1/x = 3-√8 ----------------(2)

Now We know that

(a+b)² = a²+2ab+b²

=> a²+b² = (a+b)²-2ab

On applying this for this problem

=> x²+(1/x)² = [x+(1/x)]²-2(x)(1/x)

=> x²+(1/x²) = [x+(1/x)]²-2(x/x)

=> x²+(1/x²) = [x+(1/x)]²-2

=> x²+(1/x²) = (3+√8+3-√8)²-2

=> x²+(1/x²) = (3+3)²-2

=> x²+(1/x²) = (6)²-2

=> x²+(1/x²) = 36-2

=> x²+(1/x²) = 34

Method -2:-

x = 3+√8

x² = (3+√8)²

=> x² = 3²+2(3)(√8)+(√8)²

=> x² = 9+6√8+8

=> x² = 17+6√8

and

1/x = 3-√8

=> 1/x² = (3-√8)²

=> 1/x² = 3²-2(3)(√8)+(√8)²

=> 1/x² = 9-6√8+8

=> 1/x² = 17-6√8

Now,

x²+(1/x²) = 17+6√8+17-6√8

=> x²+(1/x²) = 17+17

=> x²+(1/x²) = 34

Method-3:-

x = 3+√8

1/x = 3-√8

now,

We know that

(a+b)² + (a-b)² = 2(a²+b²)

x²+(1/x²) = (3+√8)²+(3-√8)²

=> x²+(1/x²) = 2[3²+(√8)²]

=> x²+(1/x²) = 2(9+8)

=> x²+(1/x²) = 2(17)

=> x²+(1/x²) = 34

Answer:-

The value of x²+(1/x²) = 34

Used formulae:-

• (a+b)² = a²+2ab+b²
• (a-b)² = a²-2ab+b²
• (a+b)(a-b) = a²-b²
• (a+b)² + (a-b)² = 2(a²+b²)
• The Rationalising factor of a+√b is a-√b