Math, asked by ritushende37, 1 month ago

which of the following is equivalent 81k2-64?​

Answers

Answered by PriyansuChakraborty
2

Answer:

2 solution(s) found

See steps

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:

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