if a not equal to b then show that (a+b) [1/a+1/b]
Answers
Answer:
a^3=b^3.
Step-by-step explanation:
If 1/a+1/b=1/(a+b), prove that a^3=b^3. Is this question solvable? If yes, how?
Implicit in the statement of the equation 1a+1b=1a+b is the assumption that a≠0, b≠0, and a+b≠0. What is not clear is the domain where a and b lie in.
The given equation reduces to (a+b)2=ab, and hence to a2+ab+b2=0. Thus t2+t+1=0, where t=ab. Each solution to t2+t+1=0 is also a solution to (t−1)(t2+t+1)=0, or to t3–1=0. Therefore a3=(bt)3=b3. ■
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What is 1+1-3+1-3 (1-3(1-3))?
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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THANKYOU…….
Step-by-step explanation:
(a+b)= [1/a+1/b]
then
answer will be
a+b=2/ab
(a+b) ab=2