Verify Lagrange's FormulaIf a and b are integers, (where b is not 0 or 1), verify Lagrange's Formula: a + 1 − b = ( a − 1 ) + 1 1 + 1 b − 1

Question

Verify Lagrange&#039;s FormulaIf   a and   b are integers, (where   b is not   0 or   1), verify Lagrange&#039;s Formula:  a  +            1              −        b              =  (  a  −  1  )  +            1              1        +                              1                          b              −              1

kostikvento84 · Accepted Answer

The key is to start from the right hand side  (  a  −  1  )  +      1          1      +              1                  b          −          1                      =  (  a  −  1  )  +      1                            b          −          1                          b          −          1                    +              1                  b          −          1                      =  (  a  −  1  )  +      1          b              b        −        1              =  (  a  −  1  )  +            b      −      1        b    =  (  a  −  1  )  +      b    b    −      1    b    =  (  a  −  1  )  +  1  −      1    b    =  a  −      1    b    =  a  +      1          −      b

Allyson Vance · Accepted Answer

Move   a  −  1 to the LHS to get  1  −      1    b    =      1          1      +                        1                      b            −            1                                .Then            b      −      1        b    =      1                            b          −          1          +          1                          b          −          1                      .

If a and b are integers, (where b is not 0 or 1), verify Lagrange's Formula: a+1/(−b)=(a−1)+1/(1+1/(b−1))

Open question

Answer & Explanation

New Questions in Pre-Algebra