Respuesta :

Answer:

  • x = ±0.9

Step-by-step explanation:

The algebraic identity to be used here :

  • a² - b² = (a + b)(a - b)

We know that :

  • 100x² = (10x)²
  • 81 = 9²

Therefore,

  • 100x² - 81
  • (10x + 9)(10x - 9)

The zeros are :

  • 10x + 9 = 0 ⇒ 10x = -9 ⇒ x = -9/10 ⇒ x = -0.9
  • 10x - 9 = 0 ⇒ 10x = 9 ⇒ x = 9/10 ⇒ x = 0.9
semsee45

Answer:

[tex]x=-\dfrac{9}{10} \quad x=\dfrac{9}{10}[/tex]

Step-by-step explanation:

[tex]\begin{aligned}100x^2-81 & =(10^2)x^2-9^2\\ & = (10x)^2-9^2\end{aligned}[/tex]

[tex]\textsf{Difference of Two Squares Formula}: \quad a^2-b^2=\left(a+b\right)\left(a-b\right)[/tex]

[tex]\implies a=10x \: \textsf{ and } \: b=9[/tex]

[tex]\implies 100x^2-81=(10x+9)(10x-9)[/tex]

[tex]\begin{aligned}\textsf{To find the zeros}: \quad 100x^2-81 & = 0\\\\\implies (10x+9)(10x-9) & =0\\\implies 10x+9 & =0 \implies x=-\dfrac{9}{10}\\\implies 10x-9 & =0 \implies x=\dfrac{9}{10}\end{aligned}[/tex]

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