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
Step 1: Rationalize the denominator of the given expression. To rationalize sqrt(3)2-sqrt(5), multiply the numerator and denominator by the conjugate of the denominator, which is 2+sqrt(5). sqrt(3)2-sqrt(5) = sqrt(3)2-sqrt(5) × 2+sqrt(5)2+sqrt(5) Step 2: Perform the multiplication. Multiply the numerators: sqrt(3)(2+sqrt(5)) = 2sqrt(3) + sqrt(3)sqrt(5) = 2sqrt(3) + sqrt(15) Multiply the denominators using the difference of squares formula (x-y)(x+y) = x^2 - y^2: (2-sqrt(5))(2+sqrt(5)) = 2^2 - (sqrt(5))^2 = 4 - 5 = -1 Step 3: Simplify the expression. 2sqrt(3) + sqrt(15)-1 = -(2sqrt(3) + sqrt(15)) = -2sqrt(3) - sqrt(15) Step 4: Compare the simplified expression with asqrt(b) + csqrt(d). We have -2sqrt(3) - sqrt(15). This can be written as -2sqrt(3) + (-1)sqrt(15). Comparing this to asqrt(b) + csqrt(d): a = -2 b = 3 c = -1 d = 15 All values a, b, c, d are rational numbers. The values are: a = -2 b = 3 c = -1 d = 15 Send me the next one 📸