22
If A nad B are the H.C.F and L.C.M. respectively of two algebraic expressions x and y, and A + B = x + y, then the value of $A^{3}+B^{3}$ is
- A$X^{3}-Y^{3}$
- B$X^{3}$
- C$Y^{3}$
- D$X^{3}+Y^{3}$
Answer not set
Log in or create a free account to reply and vote.
0
CCommunity
option 4 is the right answer
0
CCommunity
Let no. are x and y and HCF = A, LCM = B
Using Rule, we have
xy = AB
x + y = A + B (given) ...(i)
(x–y)2 = (x + y)2 – 4xy
or,
(x–y)2 = (A + B)2 – 4 AB
or,
(x–y)2 = (A – B)2
or,
(x–y) = A – B ...(ii)
Using (i) and (ii),
we get x = A and y = B
$A^{3}+B^{3}=X^{3}+Y^{3}$
Using Rule, we have
xy = AB
x + y = A + B (given) ...(i)
(x–y)2 = (x + y)2 – 4xy
or,
(x–y)2 = (A + B)2 – 4 AB
or,
(x–y)2 = (A – B)2
or,
(x–y) = A – B ...(ii)
Using (i) and (ii),
we get x = A and y = B
$A^{3}+B^{3}=X^{3}+Y^{3}$