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solve the algebraic inequality by wavy curve method (a) (x 2 -5x+12)/(x 2 -4x+5) >3 answer: (1/2,3)

solve the algebraic inequality by wavy curve method
(a)    (x2-5x+12)/(x2-4x+5) >3   answer: (1/2,3)

Grade:12

1 Answers

Vijay Mukati
askIITians Faculty 2590 Points
8 years ago
The discrimenant of the Quad. equation given in denomitor is < 0 and coeff. of x2 is >0. This means that expression in denominator will always give the positive value. So now in this case we can cross multiply on the other side with 3.
So, x2 – 5x + 12 > 3(x2 – 4x + 5)
or 2x2 – 7x + 3 < 0
or (2x-1) (x-3) < 0
From here using wave curve method, x will belongs in between (1/2 , 3)

Thanks

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