Question

Let \[ x = \sqrt{-4\sqrt{2} + 17 (-\sqrt{2})^2 + 2}. \] If \( x = a + b \sqrt{2} \), then what is the value of \( (a - b) \)?

• A. 0
• B. \( \frac{1}{2} \)
• C. 1
• D. \( \frac{3}{2} \)

Hint:

When dealing with square roots and radicals, carefully expand and simplify terms before trying to solve for unknowns.

Answer 1

The Correct Option is B

To solve for \( x \), simplify the given expression and solve for the values of \( a \) and \( b \). After solving, we find that \( a - b = \frac{1}{2} \).