Question

if (a+1/a) =b find a^3+3(a+1/a)+(1/a)^3 ​

Answer 1

Answer:

If 1/a+1/b=1/(a+b), prove that a^3=b^3. Is this question solvable? If yes, how?

Yes, it is solvable.

The given expression is 1/a+1/b=1/(a+b)

Therefore, by taking L. C. M on the left hand side we get,

(a+b) /ab=1/(a+b)

Now, by cross multiplication we get,

(a+b) ^2=ab

Thus,a^2+b^2+2ab=ab

Hence, a^2+b^2+2ab-ab=0

a^2+b^2+ab=0…………eqn(1)

We know, a^3-b^3=(a-b)(a^2+b^2+ab)

From eqn(1).. we get,

a^3-b^3=(a-b)*0

Hence, a^3-b^3=0.

Therefore, a^3=b^3.

HENCE PROVED.

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