Question

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

Answer 1

Answer:

-8√3

Step-by-step explanation:

(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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