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Prove that for real values of x ,(a x^2+...

Prove that for real values of `x ,(a x^2+3x-4)//(3x-4x^2+a)` may have any value provided a lies between 1 and 7.

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CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
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  7. Prove that for all real values of x and y ,x^2+2x y+3y^2-6x-2ygeq-11.

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