if 21(x2 + y2 + z2 )=(x + 2y +4z)2
find the relation between x,y,z
a)ap
b)gp
c)hp
d)none of them
problem form new pattern math-sk goyal
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1 Answers
1708\hspace{-16}$\underline{{\underline{Using $\mathbf{C. S}$ Inequality}}}::\\\\ $\mathbf{(x^2+y^2+z^2).(1^2+2^2+4^2)\geq (x+2y+4z)^2}$\\\\ and equality Hold When $\mathbf{\frac{x}{1}=\frac{y}{2}=\frac{z}{2^2}}$\\\\ So Here $\mathbf{\frac{x}{1}=\frac{y}{2}=\frac{z}{4}=k}$\\\\ i.e $\mathbf{x=k\;,y=2k,z=4k}$\\\\ Means $\mathbf{x\;,y\;,z}$ are in $\mathbf{G.P}$\\\\