Question

9.If x+y =10 and xy=21 find the value of x^3 +y^3

Answer 1

Answer:

x+y=10

therefore, (10-y)y=21

10y - $y^{2}$=21

$y^{2}$-10y+21 =0

$y^{2}$-3y-7y+21=0

y(y-3)-7(y-3)=0

(y-3)(y-7)=0

y=3 or 7

therefore

x=7 , y=3  or x=3 , y=7

In each case,

x^3 +y^3 = $3^{3}$+$7^{3}$ = 27+343 = 370

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