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
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
1). $X^{3}-Y^{3}$
2). $X^{3}$
3). $Y^{3}$
4). $X^{3}+Y^{3}$
2 answers
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
$A^{3}+B^{3}=X^{3}+Y^{3}$
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