Question

Find value of:- a) 8x^3 + y^3 - 30xy+ 125, if 2x+y=-5 b) x^3 - 27y^3 + 27, if x=3y-3

Answer 1

a) 2x+y=-5 ------------------------(1)
cubing both sides,
8x³+y³+3.2x.y(2x+y)=-125; [(x+y)³=x³+y³+3xy(x+y)]
or, 8x³+y³+6xy(-5)=-125 ; [using (1)]
or, 8x³+y³-30xy+125=0

b) x=3y-3 --------------------------(2)
cubing both sides,
x³=27y³-27-3.3y.3(3y-3) [(x-y)³=x³-y³-3xy(x-y)]
or, x³=27y³-27-27y(x) ; [using (2)]
or, x³-27y³+27=-27xy

Answer 2

Answer:

Step-by-step explanation:

A) 2x+y=-5 ------------------------(1)

cubing both sides,

8x³+y³+3.2x.y(2x+y)=-125; [(x+y)³=x³+y³+3xy(x+y)]

or, 8x³+y³+6xy(-5)=-125 ; [using (1)]

or, 8x³+y³-30xy+125=0

b) x=3y-3 --------------------------(2)

cubing both sides,

x³=27y³-27-3.3y.3(3y-3) [(x-y)³=x³-y³-3xy(x-y)]

or, x³=27y³-27-27y(x) ; [using (2)]

or, x³-27y³+27=-27xy

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