Question

18. Find the value of m if 10m - 4 = 102 × 104 using a suitable identity.

Answer 1

$$\begin{gathered} 10m-4=102\times 104 \\ \Rightarrow 10m-4=\left(100+2\right)\left(100+4\right) \\ \Rightarrow 10m-4={\left(100\right)}^2+\left(2+4\right)\times 100+2\times 4\{\mathrm{Using}\mathrm{the}\mathrm{identity}\left(x+a\right)\left(x+b\right)=x^2+\left(a+b\right)x+ab\} \\ \Rightarrow 10m-4=10000+600+8 \\ \Rightarrow 10m-4=10608 \\ \Rightarrow 10m=10608+4 \\ \Rightarrow 10m=10612 \\ \Rightarrow m=\frac{10612}{10}=1061.2 \end{gathered}$$