Question

If $x=\frac{1}{2},y=1,z=2$ then $x^{100}{y^{99}z}^{99}+x^{99}{y}^{100}{z}^{99}+x^{99}{y}^{99}{z}^{100}=..$

• A. $\frac{5}{2}$
• B. $\frac{7}{2}$
• C. $\frac{3}{2}$
• D. $\frac{9}{2}$

Answer 1

The correct option is B $\frac{7}{2}$

Given $x=\frac{1}{2},y=1,z=2$

$x^{100},y^{99}{z}^{99}+x^{99}{y}^{100}{z}^{99}+x^{99}{y}^{99}{z}^{100}$

$={\left(\frac{1}{2}\right)}^{100}\left(1{)}^{99}\right(2{)}^{99}+{\left(\frac{1}{2}\right)}^{99}\left(1{)}^{100}\right(2{)}^{99}+{\left(\frac{1}{2}\right)}^{99}\left(1{)}^{99}\right(2{)}^{100}$

$=\frac{1}{2^{100}}{2}^{99}+\frac{1}{2^{99}}{.2}^{99}+\frac{1}{2^{99}}{.2}^{100}$

$=\frac{1}{2}+1+2$

$=\frac{1+2+4}{2}$

$=\frac{7}{2}$.