Question

Find the third term to make the LHS of the
equation m2 - 3m=1 a perfect square.​

Answer 1

The third term of the LHS is $\dfrac{9}{4}$.

Step-by-step explanation:

Here, Left Hand Side is

$\quad m^{2}-3m$

$=(m)^{2}-2\times m\times\dfrac{3}{2}$

If we compare this with $(a-b)^{2}=a^{2}-2ab+b^{2}$, we get

$\quad b=\dfrac{3}{2}$

$\Rightarrow b^{2}=(\dfrac{3}{2})^{2}$

$\Rightarrow b^{2}=\dfrac{9}{4}$

So, the required third term is $\dfrac{9}{4}$.

Cheek step:

Required perfect square is

$\quad (m)^{2}-2\times m\times \dfrac{3}{2}+(\dfrac{3}{2})^{2}$

$=(m-\dfrac{3}{2})^{2}$

#SPJ3