Question

If $4a+\frac{1}{5a}=4$ , then the value of $25a^2+\frac{1}{16a^2}$ is:

• A. 55/2
• B. 45/4
• C. 45/2
• D. 33/2

Answer 1

Answer:

C. 45/2

Solution:

Given:

$4a + \frac{1}{5a}=4$

Formula used:

(a + b)² = a² + b² + 2ab

Calculation:

Multiply the given equation by $\frac{5}{4}$

$\frac{5}{4}(4a+\frac{1}{5a}) =\frac{5}{4(4)}$

⇒ $5a +\frac{1}{4a} = 5$

Squaring both sides, we get

⇒ $(5a +\frac{1}{4a}) ^2= 5^2$

⇒ $25a^2+\frac{1}{16a^2}+2(5a)(\frac{1}{4a})=25$

⇒ $25a^2+\frac{1}{16a^2}+\frac{5}{2}=25$

⇒ $25a^2+\frac{1}{16a^2}=25-\frac{5}{2}$

⇒ $25a^2+\frac{1}{16a^2}=\frac{45}{2}$

∴ The correct answer is $\frac{45}{2}$