Question

If √(x+1) + √(x – 1)= 2, then the value of x is
(1) 1/4
(2) 3/4
(3) 5/4
(4) 1​

Answer 1

Option (3)

Step-by-step explanation:

Given :-

√(x+1) + √(x – 1)= 2

To find :-

Find the value of x ?

Solution :-

Given that :

√(x+1) + √(x – 1)= 2

On squaring both sides then

=> [√(x+1) + √(x – 1)]²= 2²

=>[√(x+1)]²+[√(x-1)]²+2√[(x+1)(x-1)] = 4

Since (a+b)² = a²+2ab+b²

=> x+1+x-1+2√(x²-1) = 4

=> 2x+2√(x²-1) = 4

=> 2[x+√(x²-1)] = 4

=> [x+√(x²-1)] = 4/2

=> [x+(√x²-1)] = 2

=> √(x²-1) = 2-x

On squaring both sides again

=> [√(x²-1)]² = (2-x)²

=> x²-1 = 2²-2(2)(x)+x²

Since (a-b)² = a²-2ab+b²

=> x²-1 = 4-4x+x²

=> x²+4x-x² = 4+1

=> 4x = 5

=> x = 5/4

Therefore, x = 5/4

Answer :-

The value of x for the given problem is 5/4

Check:-

If x = 5/4 then LHS of the given equation

√(x+1) + √(x – 1)

=> √[(5/4)+1] +√[(5/4)-1]

=> √[(5+4)/4] + √[(5-4)/4]

=> √(9/4) + √(1/4)

=> (3/2) + (1/2)

=> (3+1)/2

=> 4/2

=> 2

LHS = RHS is true for x = 5/4

The equation is true for x = 5/4

Used formulae:-

• (a+b)² = a²+2ab+b²
• (a-b)² = a²-2ab+b²

Answer 2

Answer:

Thank you so much

I love you