Respuesta :
Step-by-step explanation:
To factorize the expression \(9(x-y)^2 - x^2\), you can use the difference of squares formula, which states that \(a^2 - b^2 = (a + b)(a - b)\). Apply this to your expression:
\[ 9(x-y)^2 - x^2 = (3(x-y))^2 - x^2 \]
Now, you can recognize it as a difference of squares:
\[ = (3(x-y) + x)(3(x-y) - x) \]
Therefore, the factored form is \((3x - 3y + x)(3x - 3y - x)\).
Answer:
x = 0.75 or x = 0.375
Step-by-step explanation:
[tex]9(x-y)^2-x^2[/tex]
[tex]= 9(x^2-2xy+y^2)-x^2[/tex]
[tex]= 9x^2-18xy+9y^2-x^2[/tex]
[tex]= 8x^2-18xy+9y^2[/tex]
Using Sridhar Acharya's Formula:
[tex]x = \frac{-b+\sqrt{b^2-4ac}}{2a}[/tex] and [tex]x = \frac{-b-\sqrt{b^2-4ac}}{2a}[/tex]
∴ [tex]x = \frac{18+\sqrt{18^2-(4.8.9)}}{2.16}[/tex] and [tex]x = \frac{18-\sqrt{18^2-(4.8.9)}}{2.16}[/tex]
[tex]= > x = \frac{18+\sqrt{36}}{32}[/tex] and [tex]x = \frac{18-\sqrt{36}}{32}[/tex]
[tex]= > x = \frac{24}{32} = 0.75[/tex] and [tex]= > x = \frac{12}{32} = 0.375[/tex]
