The answer is: " x = 0, 1 " . __________________________________________ Explanation: __________________________________________ Given: __________________________________________ " √(x + 1) <span>− 1 = x " ; Solve for "x" ;
First, let us assume that "x </span>≥ -1 " <span> Add "1" to EACH SIDE of the equation:
Now, substitute this "expanded" value, and bring down the "right-hand side" of the equation; and rewrite the equation: __________________________________________ " (x + 1)² = (x + 1)(x +1) " ;
→ Rewrite as: " x² + 2x + 1 = x + 1 " ;
Subtract "x" ; and subtract "1" ; from EACH SIDE of the equation:
→ x² + 2x + 1 - x - 1 = x + 1 - x - 1 ;
to get: → x² <span>− x = 0
Factor out an "x" on the "left-hand side" of the equation: ___________________________________________ </span>x² − x = x(x − 1) ;
→ x (x − 1) = 0 ;
We have: "x" and "(x − 1)" ; when either of these two multiplicands are equal to zero, then the "right-hand side of the equation equals "zero" .
So, one value of "x" is "0" .
The other value for "x" ;
→ x − 1 = 0 ;
Add "1" to each side of the equation:
→ x − 1 + 1 = 0 + 1 ;
→ x = 1 ; __________________________________ So, the answers: