Question

HCF of 126 and 35 is h. If the h is expressed as
H=126×A +35×B then prove that A×B/H = -2

Answer 1

Answer:

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, According to question,

HCF = 126A + 35B = 7

⇒18 × 7A + 5 × 7B = 7

⇒ 18A + 5B = 1 , here many solutions are 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.