LỜI GIẢI ĐỀ KIỂM TRA KHẢO SÁT THÁNG 9-NĂM HỌC 2026-2027-MÔN: TOÁN 9

OFREZH EDITOR

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CHIẾN THUẬT CHIA THỜI GIAN GIẢI ĐỀ KIỂM TRA NÀY

Python code

def solve():
    # 1) Calculate B when x = -2
    x = -2
    B_val = (3 - x) / (x - 1)
    print(f"1) B(-2) = {B_val}")

    # 2) Simplify A
    # A = (x^2 - 2x - 1)/(x^2 - 1) - (x+1)/(x-1) + 1/(x+1)
    # Let's find a common denominator: x^2 - 1 = (x-1)(x+1)
    # A = [ (x^2 - 2x - 1) - (x+1)^2 + (x-1) ] / (x^2 - 1)
    # Numerator = x^2 - 2x - 1 - (x^2 + 2x + 1) + x - 1
    #           = x^2 - 2x - 1 - x^2 - 2x - 1 + x - 1
    #           = -3x - 3
    #           = -3(x + 1)
    # So A = -3(x+1) / [(x-1)(x+1)] = -3 / (x-1)
    
    # Let's test for x = 2
    x = 2
    A_val = (x**2 - 2*x - 1)/(x**2 - 1) - (x+1)/(x-1) + 1/(x+1)
    A_simplified = -3 / (x - 1)
    print(f"2) A(2) = {A_val}, Simplified A(2) = {A_simplified}")

    # 3) P = A : B = A / B
    # P = [-3 / (x-1)] / [(3-x) / (x-1)] = -3 / (3-x) = 3 / (x-3)
    # We want P to be an integer, so (x-3) must be a divisor of 3.
    # Divisors of 3 are: 1, -1, 3, -3
    # x - 3 = 1  => x = 4
    # x - 3 = -1 => x = 2
    # x - 3 = 3  => x = 6
    # x - 3 = -3 => x = 0
    # Check conditions: x != 1, x != -1, x != 3
    # Valid values of x: 4, 2, 6, 0
    # Largest integer value of x is 6.
    
    import sympy as sp
    x_sym = sp.Symbol('x')
    A_sym = (x_sym**2 - 2*x_sym - 1)/(x_sym**2 - 1) - (x_sym+1)/(x_sym-1) + 1/(x_sym+1)
    B_sym = (3-x_sym)/(x_sym-1)
    P_sym = A_sym / B_sym
    print("Sympy Simplified A:", sp.simplify(A_sym))
    print("Sympy Simplified P:", sp.simplify(P_sym))

solve()