Question

The product of two numbers is 45 and the sum of their squares is 106. The numbers are:

• A. 3 and 5
• B. 5 and 9
• C. 5 and 19
• D. 45 and 1
• E. 3 and 19

Answer 1

Answer: (B)

5 and 9

Let the number be x and y.

Then, xy = 45

and $x^2+y^2=106.$

$\left(x+y\right)=\sqrt{\left(x^2+y^2\right)+2xy}$

$=\sqrt{106+90}$

$=\sqrt{196}$

$\therefore x+y=\mathrm{14.........}\left(i\right)$

Now, $\left(x-y\right)=\sqrt{\left(x^2+y^2\right)-2xy}$

$=\sqrt{106-90}$

$=\sqrt{16}$

$\Rightarrow x-y=\mathrm{4.........}\left(ii\right)$

Solving (i) and (ii), we get :

$x=9$ and $y=5$