Question

if a = 2+√3 find the value of a - 1/a
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Answer 1

Step-by-step explanation:

Let us assume

P = √1 + a + √1 - a

Square on both side,

P 2 = ( √1 + a + √1 - a ) 2

Use the formula ( a + b ) 2 = a 2 + b 2 + 2ab

we will get

⇒ P 2 = (1 + a) + (1- a) + 2 √1 + a x √1 - a

⇒ P 2 = (1 + a) + (1- a) + 2 √(1 + a ) x ( 1 - a )

⇒ P 2 = 2 + 2 √1 - a2

⇒ P 2 = 2 (1 + √1 - a2)

Now put the value of a which is given in question;

⇒ P 2 = 2 (1 + √1 - ( √3/2 )2)

⇒ P 2 = 2(1 + √1 - 3/4 )

⇒ P 2 = 2(1 + √1/4 )

⇒ P 2 = 2(1 + 1/2) = 2 x 3/2 = 3

⇒ P= √3

∴ (√1 + a + √1 - a) = √3