iequality 1

if a,b >0 satisfy a³+b³=a-b , then..

a) a²+b²=1

b) a²+b²>1

c) a²+b²+ab < 1

d) not.

2 Answers

341

Hari Shankar ·2009-01-16 20:32:20

a³+b³ = a-b and a,b>0. So we must have a-b>0 or a>b

a³+b³ = a³-b³+2b³

(a³+b³)/(a-b) = 1. Hence

(a³-b³+2b³) (a-b) = 1

So, (a²+ab+b²)+ 2b³/(a-b) = 1

so (a²+ab+b²)= 1 - 2b³/(a-b)<1

This also tell us that a²+b²<1

So only (c) is right

great!
thank you [1]

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