Question

State, whether the following pairs of sets equal or not:

E ={x : $x^2$ + 8x -9 =0} and F = {1, -9}

Answer 1

Step : Check whether the given pair of sets are equal
Given: E ={x : $x^2$ + 8x -9 =0}
$\Rightarrow x^2+8x-9=0$
$\Rightarrow x^2+9x-x-9=0$
$\Rightarrow x(x+9)-1(x+9)=0$
$\Rightarrow (x-1)(x+9)=0$
$\Rightarrow x=1orx=-9$
$\Rightarrow E=\{1,9\}$
And F = {1,-9} [Given]
So, elements of the sets E and F are identical.
Hence, sets E and F are equal.