Math, asked by karunashukla038, 8 months ago

if a=√3/2, then what is the value of√1+a +√1-a

Answers

Answered by Anonymous

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Answer

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 - a^2

⇒ P^2 = 2 (1 + √1 - a^2)

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

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