Question

If $a$ and $b$ are zeroes of $x^2-5x+4$, find the value of
$1/a^3+1/b^3$

Answer 1

We have,

$a$ and $b$ are zeros of

$x^2-5x+4=0$

now,

sum of zeros $=a+b=-\frac{coeffofx}{coeffof{x}^2}$

$=-\frac{-5}{1}$

$a+b=5$

product of zeros $=a.b=\frac{constantterm}{coeffof{x}^2}$

$=\frac{4}{1}$

$a.b=4$

now,

$\frac{1}{a^3}+\frac{1}{b^3}$

$\Rightarrow \frac{a^3+b^3}{a^3{b}^3}$

$\Rightarrow \frac{(a+b{)}^3-3ab(a+b)}{(ab{)}^3}$

$\Rightarrow \frac{(5{)}^3-3\times 4\times (5)}{4^3}$

$\Rightarrow \frac{125-60}{64}$

$\Rightarrow \frac{65}{64}$

Hence, this is the answer.