Respuesta :
Answer:
x - 9 = ±9
Step-by-step explanation:
We have been given the following equation;
(x-9)^2=81
We are to determine the resulting equation after taking the square root of both sides.
The square root of the expression in the left hand side is;
((x-9)^2)^(1/2)
The square and square root are inverse functions and as such they simply cancel out yielding;
x-9
Now, the square root of 81 is simply ±9 since 9*9 = 81;
9^2 = 81
Thus the square root of 81 is ±9. The resulting equation is thus;
x - 9 = ±9
This can be simplified by adding 9 on both sides of the equation to yield;
x - 9 + 9 = 9 ± 9
x = 9 ± 9
x = 9 + 9 = 18 or x = 9 - 9 = 0
x = 18 or x = 0
Answer:
[tex]\bold{x-9=\pm 9}[/tex] is the equation that results.
Step-by-step explanation:
Step 1:
[tex](x-9)^{2}[/tex]=81.
=> [tex](x-9)^{2}[/tex] - 81 = 0
=>[tex](x-9)^{2} -9^{2}[/tex]= 0
Step 2:
=> [( x - 9) + 9][( x-9)-9]=0 by the identity [tex]a^{2}-b^{2}[/tex]=(a + b) (a-b)
=> [( x - 9) + 9] = 0 or [( x - 9) - 9] = 0
=> ( x - 9) = - 9 or ( x - 9) = 9
=> x – 9 = ± 9
Step 3:
By taking square root on both side of [tex](x-9)^{2}[/tex]= 81, we get
[tex]\begin{array}{l}{\sqrt{(x-9)^{2}}=\sqrt{81}} \\ {=>(x-9)=\sqrt{9^{2}}} \\ {\Rightarrow x-9=\pm 9}\end{array}[/tex]
