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
35 Step 1: Identify the given terms and the recurrence relation. Given U_1 = 0 and U_2 = 2. The recurrence relation is U_r = U_r-1 - U_r-2. Step 2: Calculate the subsequent terms. For r=3: U_3 = U_2 - U_1 = 2 - 0 = 2 For r=4: U_4 = U_3 - U_2 = 2 - 2 = 0 For r=5: U_5 = U_4 - U_3 = 0 - 2 = -2 For r=6: U_6 = U_5 - U_4 = -2 - 0 = -2 For r=7: U_7 = U_6 - U_5 = -2 - (-2) = -2 + 2 = 0 Step 3: List the first seven terms. The first seven terms are 0, 2, 2, 0, -2, -2, 0. This matches option A. The first seven terms are A 0,2,2,0,-2,-2,0. 36 The union of set A and B is a fundamental concept in set theory. It represents a set containing all elements that are in A, or in B, or in both. The standard notation for the union of set A and set B is A B. This matches option B. The union of set A and B is B A B. 37 Step 1: Identify the coefficients of the quadratic equation. The given equation is 3y^2 - 2ysqrt(6) + 2 = 0. This is in the form ay^2 + by + c = 0, where a=3, b=-2sqrt(6), and c=2. Step 2: Calculate the discriminant . The discriminant is given by the formula = b^2 - 4ac. = (-2sqrt(6))^2 - 4(3)(2) = (4 × 6) - 24 = 24 - 24 = 0 Step 3: Determine the nature of the roots based on the discriminant. • If > 0, the roots are real and unequal. • If = 0, the roots are real and equal. • If < 0, the roots are complex (non-real). Since = 0, the roots of the equation are real and equal. This matches option A. The nature of roots of the equation are A Real and equal.