Question

The sum of two numbers is $9$ and the sum of their squares is $41$. The numbers are

• A. $4$ and $5$
• B. $1$ and $8$
• C. $3$ and $6$
• D. $2$ and $7$

Answer 1

The correct option is A $4$ and $5$

Let the numbers are x and y Then by hypothesis
$x+y=9$ ....(i)
$x^2+y^2=41$ ....(ii)
Substituting this value in equation (i) we get
$x^2{(9-x)}^2=41$
or $x^2+81-18x+x^2=41$
or $2x^2-18x+40=0$
or $x^2-9x+20=0$
or $(x-5)(x-4)=0$
$\therefore$ $x=5orx=4$
Then $y=9-x=9-5=4$
or $y=9-4=5$