What is the length of AC?
2 answers:
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Part (a):
Before we begin, remember the difference between squares rule which is as follows:
a² - b² = (a+b)(a-b)
Now, for the given we have:
1 - r⁴
This can be rewritten as:
(1)² - (r²)²
We can apply the difference between squares as follows:
(1-r²)(1+r²)
Now, checking the result we reached, we can note that we can apply the difference between squares again on the first bracket.
Doing this, we will reach:
(1-r)(1+r)(1+r²) .............> This is the simplest factored form
Part (b):
The given expression is:
6x² + 7x - 49
This is a polynomial of second degree.
This means that we can use the quadratic formula to get the solutions. The quadratic formula is shown in the attached image
From the expression, we can note that:
a = 6
b = 7
c = -49
Substituting in the formula, we would find that:
either x = 7/3 ...........> This means that the first bracket is (3x-7)
or x = -7/2 .............> This means that the second bracket is (2x+7)
Based on the above, the simplest factored form of 6x² + 7x - 49 is:
(3x-7)(2x+7)
Hope this helps :)
Before we begin, remember the difference between squares rule which is as follows:
a² - b² = (a+b)(a-b)
Now, for the given we have:
1 - r⁴
This can be rewritten as:
(1)² - (r²)²
We can apply the difference between squares as follows:
(1-r²)(1+r²)
Now, checking the result we reached, we can note that we can apply the difference between squares again on the first bracket.
Doing this, we will reach:
(1-r)(1+r)(1+r²) .............> This is the simplest factored form
Part (b):
The given expression is:
6x² + 7x - 49
This is a polynomial of second degree.
This means that we can use the quadratic formula to get the solutions. The quadratic formula is shown in the attached image
From the expression, we can note that:
a = 6
b = 7
c = -49
Substituting in the formula, we would find that:
either x = 7/3 ...........> This means that the first bracket is (3x-7)
or x = -7/2 .............> This means that the second bracket is (2x+7)
Based on the above, the simplest factored form of 6x² + 7x - 49 is:
(3x-7)(2x+7)
Hope this helps :)
We have been given a system of nonlinear equations.
In order to solve this system we can first equate the two equations in order to get a quadratic in x.
Our next step is to bring all the terms on one side.
Now we have to solve this equation. We can solve it by factoring using the splitting middle term method.
Upon setting each of these factors equal to zero using zero product property we get
Upon solving both these equations we get
Now we can substitute these values of x in the equation
We get
Therefore, our final set of solutions are