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den301095 [7]
2 years ago
13

Which equations are true for x = -2 and x = 2? Select two options

Mathematics
2 answers:
Flauer [41]2 years ago
5 0

Answer:

A and C

Step-by-step explanation:

solving the equations

A

x² - 4 = 0 ( add 4 to both sides )

x² = 4 ( take square root of both sides )

x = ± \sqrt{4} = ± 2 ← required solution

B

x² = - 4 ← has no real solutions

C

4x² = 16 ( divide both sides by 4 )

x² = 4 ( take square root of both sides )

x = ± \sqrt{4} = ± 2 ← required solution

D

2(x - 2)² = 0 , then

x- 2 = 0 ( add 2 to both sides )

x = 2 ← not the required solution

zaharov [31]2 years ago
5 0

Answer:

Answer A and C

Step-by-step explanation:

Let us solve the equations one by one and let us check whether the answers are matching with the answers given in the questions.

A) x² - 4 = 0

   ( x² - 2² ) = 0

   ( x -2 ) ( x + 2 ) = 0

   ∴ x - 2 = 0                   or           x + 2 = 0

      <u> x = 2  </u>                                     <u>x = -2 </u>               <em>( Matched )</em>

B) x² = -4

  <u> x = ±√-4  ← no real solutions  </u>                  (<em>Not matched )</em>

B)   3x² + 12 = 0

      3 ( x² + 4 ) = 0

      <u>3 ( x² + 2² ) = 0 ← no real solutions   </u>    (<em>Not matched)</em>

C) 4x² = 16

Divide both sides by 4.

 x² = 4

 x = ±√4

 ∴ <u>x = 2  </u>       or        <u>x = -2</u>      <em> (Matched)</em>

 D) 2 ( x - 2 )² = 0    

      (2x - 4)² = 0

      4x² - 16x + 16 = 0

<em>Divide the whole equation by 4.</em>

   x² - 4x + 4 = 0

 x² - 2x - 2x + 4 = 0

x ( x - 2 ) - 2 ( x - 2 ) = 0

( x - 2 ) ( x - 2) =

∴ x - 2 = 0          or        x - 2 = 0

 <u> x = 2 </u>                           <u> x = 2 </u>                 <em>( Not matched )</em>

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