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Grade 10

Two radicals, one quadratic

Two square roots that look unrelated are wearing the same quadratic underneath. Spot it and the whole equation collapses; then find how the two roots relate.

  1. 1

    Find k

    Consider the equation 3x2−8x+1+9x2−24x−8=3.\sqrt{3x^2 - 8x + 1} + \sqrt{9x^2 - 24x - 8} = 3. The largest real root is −k-k times the smallest real root. Find kk.