Hello ShadowWolfie!
[tex] \huge \boxed{\mathbb{QUESTION} \downarrow}[/tex]
Solve the equation with special factors.
x² - 81 = 0.
[tex] \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}[/tex]
You can solve this question using 3 methods :-
- By using the quadratic formula.
- By finding the square root.
- By using the difference of the squares.
Let's take a look at all the 3 methods.
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1. By Using Quadratic Formula :-
[tex]x ^ { 2 } - 81 = 0[/tex]
We can use the biquadratic formula straight away as it is already in the form of ax² + bx + c. Now, we know that the biquadratic formula is :- [tex]\frac{ - b \: ± \: \sqrt{ {b}^{2} - 4ac} }{2a}[/tex]. In this equation..
Now, substitute these values in the formula..we get..
[tex] \\ x=\frac{0±\sqrt{0^{2}-4\left(-81\right)}}{2} [/tex]
Let's simplify it.
[tex]x=\frac{0±\sqrt{0^{2}-4\left(-81\right)}}{2} \\ x=\frac{0±\sqrt{-4\left(-81\right)}}{2} \\ x=\frac{0±\sqrt{324}}{2} \\ x=\frac{0±18}{2} \\ \boxed{\boxed{ \bf \: x = ±9}}[/tex]
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2. By Finding The Square Root :-
[tex]x ^ { 2 } - 81 = 0[/tex]
Add zero to both the sides..our equation will become..
[tex]x^{2}=81 [/tex]
Now, take the square root on both the sides.
[tex]x^{2}=81 \\ \sqrt{ {x}^{2} } = \sqrt{81} \\ \boxed{ \boxed{\bf x = ±9}}[/tex]
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3. By Using The Difference of The Squares :-
[tex]x ^ { 2 } - 81 = 0[/tex]
Let's rewrite this equation as :- x² - 9². Now let's solve it using the algebraic identity ⇨ a² - b² = (a + b) (a - b). So..
[tex]x ^ { 2 } - 81 = 0 \\ {x}^{2} - {9}^{2} = 0 \\ \left(x-9\right)\left(x+9\right)=0 [/tex]
Let's solve for each term..
[tex](x - 9) = 0 \\ \underline{ \underline{x = + 9}}[/tex]
And..
[tex](x + 9) = 0 \\ \underline{ \underline{x = - 9}}[/tex]
So,
[tex]\boxed{ \boxed{\bf x = ±9}}[/tex]
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- By using the 3 different methods (you can choose whichever method you find is easier), we got the answer as x = ± 9 .
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Hope it'll help you!
ℓu¢αzz ッ
