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Quadratic function in Senior High School It is known that the parabola y = (m-1) x ^ 2 + (m-2) X-1, (m ∈ R) (1) If the sum of the reciprocal squares of the two unequal real roots of the equation (m-1) x ^ 2 + (m-2) X-1 = 0 is greater than 2, the value range of M is obtained (2) If the parabola intersects the x-axis at points a and B, intersects the y-axis at point C, and the area of △ ABC is equal to 2, try to find the value of M
1. Let a and B be the two roots of the equation
Then m ≠ 1, Δ = (m-2) & sup2; + 4 (m-1) > 0 ①
And 1 / A & sup2; + 1 / B & sup2; = [(a + b) & sup2; - 2Ab] / (A & sup2; B & sup2;) > 2
Substituting a + B = - (m-2) / (m-1), ab = - 1 / (m-1) into the above formula, m (m-2 > 0) ①
The solution is m
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