If $x^2+4 y^2=53$ and $x-2 y=5$, then what is the value of $x^3-8 y^3$ ?
Answer & explanation
Correct answer: option 2
If $x^2+4 y^2=53$ and $x-2 y=5$,
What is the value of $x^3-8 y^3$
( a - b )2 = a2 + b2 - 2×2ab
(5 )2 = 53 - 4ab
4ab = 28
ab = 7
If x - y = n
then, $x^3 - y^3$ = n3 + 3 × n × xy
$x^3-8 y^3$ = 53 + 3 × 5 × 2 × 7
$x^3-8 y^3$ = 125 + 210
$x^3-8 y^3$ = 335