This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Alright andyjenniferebot — let's do this. Step 1: Evaluate the powers of (1)/(sqrt(2)). ((1)/(sqrt(2)))^3 = (1^3)/((sqrt(2))^3) = (1)/(2sqrt(2)) Step 2: Substitute this value back into the expression. 2((1)/(2sqrt(2))) - 3((1)/(sqrt(2))) + 1 Step 3: Simplify the terms. (2)/(2sqrt(2)) - (3)/(sqrt(2)) + 1 = (1)/(sqrt(2)) - (3)/(sqrt(2)) + 1 Step 4: Combine the fractions. (1-3)/(sqrt(2)) + 1 = (-2)/(sqrt(2)) + 1 Step 5: Rationalize the denominator of the fraction. (-2)/(sqrt(2)) × sqrt(2)sqrt(2) = -2sqrt(2)2 = -sqrt(2) Step 6: Perform the final addition. -sqrt(2) + 1 = 1 - sqrt(2) The simplified expression is: 1 - sqrt(2) What's next? 📸