Q36 / 89 · KVPY 2017 (5 Nov SB/SX) · Mathematics

Suppose $p, q, r$ are real numbers such that $q=p(4-p), r=q(4-q), p=r(4-r)$ The maximum possible value of $\mathrm{p}+\mathrm{q}+\mathrm{r}$ is

A
0
B
3
Correct answer
C
9
D
27

Solution

Add all these $p+q+r=\frac{p^{2}+q^{2}+r^{2}}{3}$ for maximum value $\mathrm{p}=3, \mathrm{q}=3, \mathrm{r}=3$ Answer is 9 .

Hence, the correct answer is option: 'C'.

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