Question

X+y=7, xy=10 then find x3+y3/x3y3

Answer 1

$\boxed{\textbf{\large{Explanation:}}}$

(x³ + y³ ) = (x + y) (x² - xy + y² )

we have,

x + y = 7 , xy = 10

we know,

( x + y) ² = x² + 2xy + y²

(x + y)² - (2xy) = (x² + y² )

( 7)² - (2 x 10 ) = (x² + y² )

49 - 20 = (x² + y² )

29 = (x² + y² )

therefor,

(x³ + y³ ) = (x + y) (x² - xy + y² )

= )) ( 7) ( (x² + y²) - xy)

=)) (7) ( (29 ) - (10))

=)) (7) x (19)

(x³ + y³ ) = 133

(x³ x y³ ) = (xy) ³ = (10)³ = 1000

therefor,

(x³ + y³ ) / (x³y³) = 133 / 1000

= )) 133 x (10^(-3))

=)) 0.133

(x³ + y³ ) / (x³y³) = 0.133