Question

Q19.
I
If a=2+✓3 then find the value of a²+1/a²​

Answer 1

EXPLANATION.

⇒ a = 2 + √3.

As we know that,

We can write equation as,

⇒ 1/a = 1/(2 + √3).

Now, rationalize the equation, we get.

⇒ 1/a = 1/(2 + √3) x (2 - √3)/(2 - √3).

⇒ 1/a = (2 - √3)/[(2)² - (√3)²].

⇒ 1/a = (2 - √3)/[4 - 3].

⇒ 1/a = (2 - √3)/1 = 2 - √3.

To find :

⇒ a² + 1/a².

⇒ a² = (2 + √3)².

⇒ a² = 4 + 3 + 4√3.

⇒ a² = 7 + 4√3.

⇒ 1/a² = (2 - √3)².

⇒ 1/a² = 4 + 3 - 4√3.

⇒ 1/a² = 7 - 4√3.

⇒ (a² + 1/a²) = [(7 + 4√3) + (7 - 4√3].

⇒ (a² + 1/a²) = [7 + 4√3 + 7 - 4√3].

⇒ (a² + 1/a²) = 14.

Answer 2

✫SOLUTION✫

a=2+✓3

1/a=1/2+ ✓3

By rationalization,

1 / x = 2 - ✓3

Now,

a ^ 2 + 1 / a ^ 2

2+ ✓3^ 2 +2- ✓ 3^ 2

4 + 3 + 4✓3 + 4 + 3 - 4✓3

4 + 3 + 4 + 3

= 14.

☢︎︎WHICH IS THE REQUIRED ANSWER☢︎︎

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