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a^3 – 3a^2 + 5a =1 and b^3 – 3b^2 + 5b =5 then (a+b) is equal to

 
a^3 – 3a^2 + 5a =1 and b^3 – 3b^2 + 5b =5
then (a+b) is equal to

Grade:

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
7 years ago
Hello student,
Please find the answer to your question below
Givena^3 – 3a^2 + 5a =1 and b^3 – 3b^2 + 5b =5
Soa^3 – 3a^2 + 3a-1=-2a......(1)
b^3 – 3b^2 + 3b-1 = -2b+4......(2)
From 1,2 we have (a-1)3=-2a....(3)
(b-1)3=-2b+4....(4)
Let x=a-1 and y=b-1
So from 3 x3=-2(x+1) So x3+2x+2=0.........(5)
From 4 we have y3=-2(y+1)+4
y3+2y-2=0....(6)
Adding 5 and 6 we get
x3+y3+2x+2y=0
x+y(x2-xy+y2)=0
So x+y=0 or x2-xy+y2=0
If x+y=0 we get a-1+b-1=0
So a+b=2

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