Madhya Pradesh Police Exam Model Paper 7

Given:
Product of two numbers = 48
Sum of their square = 100
Concept used:
${\left(\mathit{a}+\mathit{b}\right)}^2={\mathit{a}}^2+2\mathit{a}\mathit{b}+{\mathit{b}}^2$
Calculations:
Let the number be x and y
According to the questions,
$\mathit{x}\times \mathit{y}=48$ ----(1)
Multiply equation (1) with 2
$2\mathit{x}\mathit{y}=96$ ----(2)
${\mathit{x}}^2+{\mathit{y}}^2=100$ ----(3)
Add equation (2) and (3)
${\mathit{x}}^2+{\mathit{y}}^2+2\mathit{x}\mathit{y}=100+96$
$\Rightarrow {\left(\mathit{x}+\mathit{y}\right)}^2=196$
$\Rightarrow \left(\mathit{x}+\mathit{y}\right)=\surd 196$
$\Rightarrow \mathit{x}+\mathit{y}=14$
∴ The sum of these two numbers is 14