Question

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> The sum of two numbers is 9 and their product is 20 . Find the sum of their (i) Squares (ii) Cubes

Answer 1

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Given, the sum of two numbers is 9 and their product is 20 Let's assume the numbers to ' $a$ ' and 'b'
So, we have
$a+b=9\dots \left(1\right)$ and
$ab=20\dots$ (2)
Now,
On squaring (1) on both sides gives, we get
$(a+b{)}^2=9^2$
$a^2+b^2+2ab=81$
$a^2+b^2+2\left(20\right)=81\dots$ [From (2)]
$a^2+b^2+40=81$
$a^2+b^2=81-40=41$
(i) Hence, the sum of their squares is 41
Next,
On cubing (1) on both sides, we get
$$(a+b{)}^3=9^3$$
$$a^3+b^3+3ab(a+b)=729$$
$a^3+b^3+3\times \left(20\right)\times \left(9\right)=729\dots$ [From (1) and (2)]
$a^3+b^3=729-540=189$
(ii) Hence, the sum of their cubes is 189 .