The maximum value of the expression 1343x-7-3x is

1343^x+7^ 3x ⇒17^3x+7^ 3x This value will be max when 7^3x+7^ 3x is minimum. Now, using (a+b)^2≥4ab nbsp; nbsp; (7^3x+7^ 3x)^2≥4 ⇒7^3x+7^ 3x≥2 Maximum valu ...

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Standard XII

Mathematics

Properties of Inequality: Squaring or Raising Inequalities to Certain Power

The maximum v...

Question

The maximum value of the expression $\frac{1}{343^{x} + 7^{- 3 x}}$ is

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Solution

$\frac{1}{343^{x} + 7^{- 3 x}}$
$\Rightarrow \frac{1}{7^{3 x} + 7^{- 3 x}}$
This value will be max when $7^{3 x} + 7^{- 3 x}$ is minimum.

Now, using $(a + b)^{2} \geq 4 a b$
$(7^{3 x} + 7^{- 3 x})^{2} \geq 4$
$\Rightarrow 7^{3 x} + 7^{- 3 x} \geq 2$
Maximum value of $\frac{1}{7^{3 x} + 7^{- 3 x}} = 0.5$

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The maximum value of the expression 1343x+7−3x is

1343x+7−3x ⇒173x+7−3x This value will be max when 73x+7−3x is minimum. Now, using (a+b)2≥4ab (73x+7−3x)2≥4 ⇒73x+7−3x≥2 Maximum value of 173x+7−3x=0.5

The maximum value of the expression $\frac{1}{343^{x} + 7^{- 3 x}}$ is