which of the following is equivalent 81k2-64?
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Answer:
2 solution(s) found
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Step by Step Solution
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Reformatting the input :
Changes made to your input should not affect the solution:
(1): "k2" was replaced by "k^2".
Step by step solution :
STEP
1
:
Equation at the end of step 1
34k2 - 64 = 0
STEP
2
:
Trying to factor as a Difference of Squares:
2.1 Factoring: 81k2-64
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 81 is the square of 9
Check : 64 is the square of 8
Check : k2 is the square of k1
Factorization is : (9k + 8) • (9k - 8)
Equation at the end of step
2
:
(9k + 8) • (9k - 8) = 0
STEP
3
:
Theory - Roots of a product
3.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
Solving a Single Variable Equation:
3.2 Solve : 9k+8 = 0
Subtract 8 from both sides of the equation :
9k = -8
Divide both sides of the equation by 9:
k = -8/9 = -0.889
Solving a Single Variable Equation:
3.3 Solve : 9k-8 = 0
Add 8 to both sides of the equation :
9k = 8
Divide both sides of the equation by 9:
k = 8/9 = 0.889
Two solutions were found :
k = 8/9 = 0.889
k = -8/9 = -0.889
Step-by-step explanation: