Class 11

Math

Algebra

Sequences and series

If *G* is the geometric mean of *x* and *y*, then

$tG_{2}−x_{2}1 +G_{2}−y_{2}1 =G_{2}1 $

**Solution: **$G_{2}=xy$

$∴$LHS=

$G_{2}−x_{2}1 +G_{2}−y_{2}1 $

$=xy−x_{2}1 +xy−y_{2}1 $

$=x(y−x)1 −y(y−x)1 $

$=y−x1 [x1 −y1 ]$

$=y−x1 [xyy−x ]$

$=xy1 $

$=G_{2}1 =$RHS

Hence, proved