Question

Given that $a(a+b)=36$ and $b(a+b)=64$, where $a$ and $b$ are positive, $(a-b)$ equals:

• A. $2.8$
• B. $3.2$
• C. $-2.8$
• D. $-2.5$

Answer 1

The correct option is C $-2.8$

Given, $a(a+b)=36$ and $b(a+b)=64$
By adding both,
$a(a+b)+b(a+b)=36+64$
$\Rightarrow a^2+ab+ab+b^2=100$
$\Rightarrow a^2+2ab+b^2=100$
$\Rightarrow {(a+b)}^2=100$
$\Rightarrow a+b=10(a+b\ne -10)$
Now replacing $a+b$ value in above equation:
$\Rightarrow a\left(10\right)=36$ and $b\left(10\right)=64$
$\Rightarrow 10a=36$ and $10b=64$
$\Rightarrow 10(a-b)=36-64$
$\Rightarrow 10(a-b)=-28$
$\therefore a-b=-2.8$