Question
If $a + b = 25$ and $a^2+ b^2= 225$, then find $ab$.
✓
Answer
Given,
$a + b = 25$ and $a^2+ b^2= 225$
$(a + b)^2= a^2+ b^2+ 2ab (25)^2$
$= 225 + 2ab 2ab$
$= (25)^2- 225 2ab$
$= 625 - 225 2ab$
$= 400$
$2\text{ab}=\frac{400}{2}$
$= 200$
$a + b = 25$ and $a^2+ b^2= 225$
$(a + b)^2= a^2+ b^2+ 2ab (25)^2$
$= 225 + 2ab 2ab$
$= (25)^2- 225 2ab$
$= 625 - 225 2ab$
$= 400$
$2\text{ab}=\frac{400}{2}$
$= 200$
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