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do max and min questions come in IITJEE a 2 +4b 2 =4 find the max value of 3a+2b-2

do max and min questions come in IITJEE
 
a2+4b2=4
find the max value of 3a+2b-2

Grade:11

2 Answers

raj
384 Points
5 years ago
hello rahul,
in the first given equation a2+4b2=4 put a=0 we get b=1 put b=0 we get a=2
then substitute in the 3a+2b-2 we get 6
jagdish singh singh
173 Points
5 years ago
\hspace{-0.6 cm}$Using $\bf{Cauchy\; Schwartz}$ Inequality,\\\\$\left\{a^2+(2b)^2\right\}\cdot (3^2+1^2)\geq (3a+2b)^2\Rightarrow (3a+2b)^2\leq 4\cdot 10$\\\\So we get $3a+2b\leq 2\sqrt{10}\Rightarrow 3a+2b-2\leq 2\left(\sqrt{10}-1\right)$\\\\ and equality hold when $\frac{a}{3}=\frac{2b}{1}.$

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