Question : If $16 y^2-k=\left(4 y+\frac{3}{2}\right)\left(4 y-\frac{3}{2}\right)$, then the value of $k$ is:
Option 1: $\frac{9}{4}$
Option 2: $\frac{11}{4}$
Option 3: $\frac{6}{4}$
Option 4: $\frac{7}{4}$
Answer (1)
27th Jan, 2024
Correct Answer: $\frac{9}{4}$
Solution :
$16 y^2-k=\left(4 y+\frac{3}{2}\right)\left(4 y-\frac{3}{2}\right)$
$⇒(4y)^2-k=(4y)^2-(\frac{3}{2})^2$
$⇒k=(\frac{3}{2})^2$
$\therefore k = \frac{9}{4}$
Hence, the correct answer is $\frac{9}{4}$.
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