Question

HCF of 126 and 35 is H and H= 126*A+35*B so show that A*B/H=-2

Answer 1

$$\begin{gathered} 126=2\times 3\times 3\times 7 \\ 35=5\times 7 \\ \mathrm{HCF}\mathrm{of}126\mathrm{and}35=7 \\ \mathrm{Therefore},7=126A+35B \\ \Rightarrow 7=7\left(18A+5B\right) \\ \Rightarrow 1=18A+5B \\ \mathrm{It}\mathrm{is}\mathrm{true}\mathrm{for}A=2\mathrm{and}B=-7 \\ \mathrm{Now}, \\ \frac{A\times B}{H}=\frac{2\times \left(-7\right)}{7}=-2 \\ \mathrm{Hence},\mathrm{proved}. \end{gathered}$$