Question

if a = 2+√3, then a^2+1/a^2

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

Answer:

$\underline{\purple{\ddot{\Mathsdude}}}$

☆Answered by Rohith kumar maths dude: -

▪Here given that,

a=2+root3.

▪This equation we can write it as,

=1/a=1/(2+root3).

▪Next by rationalizing the equation we get that,

1/a=1/2+root3)×(2-root3)/(2-root3)

1/a=1/2+root3/[(2)^2-(root3)^2

1/a=2-root3/(4-3)

1/a=2-root3/1

=2-root3.

.

▪Next, we should find that,

a^2+1/a^2

a^2=(2+root3)^2

▪By equating this equation we get that,

a^2=7+4root3.

.

▪And ,

1/a^2=(2-root3)^2.

▪And also equating this equation we get that,

1/a^2=7-4root3.

☆Next by applying the answers to the in the given question

,

☆we get ,

a^2+1/a^2=[(7+4root3)+(7-4root3)]

a^2+1/a^2=[7+4root3+7-4root3]

a^2+1/a^2=14..

☆Refer it if u got any problem ask me ok .

☆Thank you.

☆Hope it helps u mate.