Question

a= √3/2 then the value of √1+a +√1-a​

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

Answer 2

Answer:

See below:-

Step-by-step explanation:

Answer is √2

Just assume the answer be x.

And put the value as given .

Square both sides and then in last square root the value of x.