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if x^2+y^2=25 And x^3+y^3=91, Find the value of x and y .
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Answer:
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Step-by-step explanation:
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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).