Answer:
Yes it does
Step-by-step explanation:
we would like to Prove the following for x=1:
[tex] \displaystyle {x}^{2} - x = 0[/tex]
since x=1 substitute:
[tex] \displaystyle {1}^{2} - 1 \stackrel {?}{=}0[/tex]
to simplify it we can consider the order of PEMDAS which is a abbreviation of
- Parentheses
- Exponent
- Multiplication or
- Division
- Addition or
- Substraction
since exponent come first
simplify exponent:
[tex] \displaystyle {1}^{} - 1 \stackrel {?}{ = }0[/tex]
simplify substraction:
[tex]\displaystyle 0 \stackrel { \checkmark}{ = }0[/tex]
since left hand side equal to right hand side
hence, Proven
Alternate way:
use a²-b²=(a+b)(a-b) to rewrite:
[tex] \displaystyle (x + \sqrt{x} )(x - \sqrt{x} ) = 0[/tex]
since x=1 substitute:
[tex] \displaystyle (1 + \sqrt{1} )( 1- \sqrt{1} ) \stackrel {?}{=} 0[/tex]
simplify square root:
[tex] \displaystyle (1 + 1)( 1- 1 ) \stackrel {?}{=} 0[/tex]
simplify parentheses:
[tex] \displaystyle (2)( 0) \stackrel {?}{=} 0[/tex]
Multiplying any number by 0 results 0 thus
[tex] \displaystyle 0 \stackrel { \checkmark}{=} 0[/tex]
since left hand side equal to right hand side
hence, Proven
