Find all real solutions of the equation. x-\sqrt{x-1}=3

Armorikam

Armorikam

Answered question

2021-09-28

Find all real solutions of the equation.
xx1=3

Answer & Explanation

odgovoreh

odgovoreh

Skilled2021-09-29Added 107 answers

Step 1
The given equation is,
xx1=3
We need to find the real solution to the given equation.
Step 2
On solving the equation, we get
xx1=3
x3=x1
On squaring both the sides, we get
(x3)2=(x1)2
x2+96x=x1
x26x+9x+1=0
x27x+10=0
x25x2x+10=0
x(x5)2(x5)=0
(x2)(x5)=0
Hence, the solution of the equation are as,
x2=0
x=2...(i)
And,
x5=0
x=5...(ii)
Therefore, the solutions are 2 and 5.

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