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    Question

    AB is parallel to DC in a trapezium ABCD. It is given

    that AB > DC and the diagonals AC and BD intersect at O. If AO = 3x - 15 OB = x + 9, OC = x - 5 and OD = 5, and x has two values x1 and x2 then the value of ( x12┬а+ x22) is:
    A 45 Correct Answer Incorrect Answer
    B 61 Correct Answer Incorrect Answer
    C 73 Correct Answer Incorrect Answer
    D 56 Correct Answer Incorrect Answer

    Solution

    ATQ, тЗТ (3x - 15) ├Ч 5 = (x + 9) ├Ч (x - 5) тЗТ 15x - 75 = x2┬а+ 9x - 5x - 45 тЗТ 15x - 75 = x2┬а+ 4x - 45 тЗТ x2┬а- 11x + 30 = 0 Solving the quadratic equation: тЗТ x1┬а= 6, x2┬а= 5 To find x12┬а+ x22: тЗТ 62┬а+ 52┬а= 36 + 25 = 61

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