Question

Solve the radical equation.
√x+3-1= x

Answer 1

x = 1

Explanation:

Radical expression:

• √(x+3)-1 = x

Let's find the value of x.

Solved:

√(x+3)-1 = x

Transpose -1 to RHS:

• => √(x+3) = x+1

Squaring both LHS and RHS,we have:

• => √(x+3)^2= (x+1)^2
• => x+3 = x²+2x+1

Subtracting x^2+2x+1 from both sides,we have:

• =>x+3−(x²+2x+1)=x²+2x+1−(x²+2x+1)
• => −x^2−x+2=0

Factoring LHS,we have:

• =>(−x+1)(x+2)=0

Setting (-x+1) = 0 and (x+2) = 0 each time:

• =>(-x+1) = 0
• => x-1 = 0
• => x = 0+1
• => x=1

Now

• => (x+2) = 0
• => x= 0-2
• => x = -2

There are two solutions– (1,-2)

Let's plug to the given equation to check.

x = 1 :

√(x+3) -1 = x

• √(1+3)-1 = 1
• √4 - 1 = 1
• 2 - 1 = 1
• 1 = 1

Equation is true,when plugged to x = 1.

x = -2:

√(x+3) -1 = x

• √(2+3) - 1 = -2
• √5 -1 = -2
• 2.23606 - 1 = -2
• 1.236 = -2

Equation is false,when plugged to x = -2.

Hence,the value of x is 1.

-Regards,Hannah