Question

X^3+y^3=25 than x^3-y^3=

Answer 1

Answer:

Step-by-step explanation:

 

Let x+y=t

Now squaring both sides,

t2 = x2+y2+2xy = 25+2xy(from eqn 1)

Hence

t2=25+2xy

(Call this result 1)

Now cube t

t3=x3+y3+3x2y+3xy2

t3=91+3xy(x+y)

                             =91+3xyt

Now from result 1 we know xy in terms of t. Substituting in above,

we get  cubic in t,

t3−75t+182=0

On solving for t,

we get 3 solns

t=7,  -9.68465843842649,  2.68465843842649

Now we know t = x+y,

on substituting for t in result 1 ,we get the value of xy.

As we know now xy and (x+y) we can solve for x and y.

On solving we get

1)t=7,  x=3,y=4

2)t=-9.68465843842649

x= -4.842+3.308i

y=-4.842-3.308i ( approximately)

3)t= 2.68465843842649

x=4.613

y=-1.92847 ( approximately)

                           

Note that in all above solutions that x and y can e interchanged giving us 6 possible (x,y).