Question

a³ + 1/b³ = 18 হলে a = কত ?
বি.দ্রঃ a এর মান দেয়া নাই ।

Answer 1

Step-by-step explanation:

There are a continuum of solutions to

a3+b3+3ab=1

Suppose that

x=a+b

then

1 =a3+(x−a)3+3a(x−a) =x3−3ax2+3a2x+3ax−3a2

which means

0 =(x−1)(x2+(1−3a)x+3a2+1)

So either x=1 irregardless of a, or

x=

3a−1±(a+1)

√

−3

2

Thus, other than x=1, the only real x is −2, which comes from a=−1.

That is, the only two real values of a+b are 1 and −2.

Answer 2

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