Question

the hcf of 126 and 35 is H.if H is expressed as H= 126*A+35*B then prove that A*B/H=-2

Answer 1

HCF of 126 and 35 :-

Prime Factors of 35 = 5 × 7
Prime factors of 126 = 2 × 3 × 3 × 7
∴ common factors = 7
∴ HCF = common factors = 7

Now, A/C to question,
HCF = 126A + 35B = 7
⇒18 × 7A + 5 × 7B = 7
⇒ 18A + 5B = 1 , here many solutions possible because given one equation and two variables.
Let A = 2 and B = -7 then, 18 × 2 - 5 × 7 = 1
So, A = 2 and B = -7 is A solution of this equation .

Now, LHS = A.B/H
PUT A = 2 , B = -7 and H = 7
Then, A.B/H = 2 × -7/7 = -2 = RHS
Hence , proved//

Answer 2

Proved that $\frac{A*B}{H} = - 2$.

To prove :   $\frac{A*B}{H} = - 2$

Given :

          HCF of 126 and 35 is H.

Where, "H" is the common factor of 126 and 35.

To find H :

                126 = 2 × 3 × 3 × 7

                  35 = 5 × 7

Hence, the common factor "H" is  "7".

            126 A + 35 B = 7  -----> eqn (1)

Take common values from "126 A + 35 B = 7"

It gives,         7 (18A + 5B) = 7

LHS = 7 and RHS =7 get cancel each other, which gives

                           18A + 5B = 1  -----> eqn (2)

Compare the equation (1) and (2),

                              126 A + 35 B = 7                                            

                                  18A + 5B    = 1

We get, A = 2 and B = -7

Substitute, the value of A and B in $\frac{A*B}{H} = - 2$

               

                  $\frac{2*(-7)}{7} = - 2$

                  $\frac{-14}{7} = -2$

                  $- 2 = -2$

                 LHS = RHS

Thus, the expression has been proved.    

To learn more...

brainly.in/question/3422868