Thebecksidn
Answered

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If x = 1 does x² - x = 0?

Sagot :

Nayefxidn

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

Blackshadesidn

Given,

x = 1

We need to find if x² - x = 0 is true or false.

If x = 1, then x² will be equal to 1² = 1 (1 multiplied by 1 is one / 1 square is equal to 1)

So,

=》x² - x = 0

By substituting ...

=》1² - 1 = 0

Now calculate...

=》1 - 1 = 0

=》0 = 0

•°• The given statement is true.

_____

RainbowSalt2222 ☔

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