Question

If a = 2 + √3 , then find the value of a2 - 1/a2

Answer 1

Answer:

-8√3

Step-by-step explanation:

★a² –1/a²

= (a)²–(1/a)²

= ( a+1/a) (a–1/a)

= (2+√3+1/2+√3) (2+√3–1/2+√3)

= [{(2+√3)²-1}\1] [{(2+√3)²-1}\1]

= [{(2)²+(√3)²+2×2×√3+1}\2+√3] [{(2)²+(√3)²+2×2×√3+1}/2+√3]

= [(4+3+4√3+1)/2+√3] [(4+3+4√3–1)/2√3]

= [(8+4√3)/2+√3] [(6+4√3)/2+√3]

= [(8+4√3)(2–√3)/(2+√3)(2–√3)] [(6+4√3)(2–√3)/(2+√3)(2–√3)]

= [(16–8√3+8√3–12)/4–3] [(12–6√3+8√3–12)/4–3]

= 4(–2√3)

=–8√3

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Answer 2

Step-by-step explanation:

Given that,

a=2+

3

Then, Value of

a−

a

1

=2+

3

−

2+

3

1

=2+

3

−

2+

3

1

×

2−

3

2−

3

onrationalize

=2+

3

−

4−3

(2−

3

)

=2+

3

−2+

3

=2

3

Hence, this is the answer.