Question

root x-1 +root x+1 +1 =0 then 4x is equal to

Answer 1

√x-1 + √x+1 +1=0
√x-1=-1-√x+1
squaring
x-1= 1+2√x+1+x+1
-3=2√x+1
squaring
9=4(x+1)
4x=5
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Answer 2

The value 4x=5

Step-by-step explanation:

Given equation is  $\sqrt{x-1}+\sqrt{x+1}+1=0$

To find the value of 4x :

Solving the given equation as below :

• $\sqrt{x-1}+\sqrt{x+1}+1=0$
• $\sqrt{x-1}+1=-\sqrt{x+1}$

Squaring on both the sides we get

• $(\sqrt{x-1}+1)^2=(-\sqrt{x+1})^2$
• $(\sqrt{x-1})^2+2(\sqrt{x-1})(1)+1^2=x+1$ ( using the identities $(a+b)^2=a^2+2ab+b^2$ and by $(\sqrt{a})^2=a$ )

• $x-1+2(\sqrt{x-1})+1=x+1$
• $x-1+2(\sqrt{x-1})+1-x-1=0$
• $2(\sqrt{x-1})+1=0$ ( by adding the like terms )
• $2(\sqrt{x-1})=-1$

Squaring on both the sides we get

• $(2(\sqrt{x-1}))^2=(-1)^2$
• $2^2(x-1)=1$ ( by using $(ab)^2=a^2.b^2$ )
• $4(x-1)=1$
• $4x+4(-1)=1$ ( by using the distributive property a(x-y)=ax-ay )
• $4x-4=1$
• $4x=1+4$ ( adding the like terms )
• $4x=5$

Therefore the value of 4x is 5