Can the Property of this:
ax2 + bx + c = 0
(a+b)(a-b) = 0
a = -b , a = b
BE FURTHER APPLIED TO THIS.....:?
ax2 + bx + 8 = 0
-------------------------
-8 -8
x (ax + b) = 8
x = 8 , x = (8-b)/a
Thank you!
To apply the property you mentioned to the equation ax^2 + bx + 8 = 0, we need to notice that in the equation (a+b)(a-b) = 0, the left side can be factored as a difference of squares.
Now let's apply the difference of squares property to the equation ax^2 + bx + 8 = 0:
First, we need to find the factors of 8 that will give us the middle term bx when multiplied together. The factors of 8 are:
1 and 8
2 and 4
To use the difference of squares, we want the product of the factors to be negative. So we can either choose 1 and 8 or 2 and 4, but one factor should be positive and the other negative.
Now, rewrite the middle term bx using the chosen factors. Let's assume we choose 1 and 8:
bx = (x * 8) + (x * 1) = 8x + x = 9x
We can rewrite the equation as:
ax^2 + 9x + 8 = 0
Now, we can apply the difference of squares property:
(ax + 8)(ax - 1) = 0
From this equation, we can extract two possible solutions:
1. ax + 8 = 0
ax = -8
x = -8/a
2. ax - 1 = 0
ax = 1
x = 1/a
So the possible solutions for the equation ax^2 + bx + 8 = 0 are:
x = -8/a and x = 1/a