For the following questions answer them individually
Which of the following statement(s) is/are TRUE?
I. $$\surd5 + \surd5 > \surd7 + \surd3$$
II. $$\surd6 + \surd7 > \surd8 + \surd5$$
III. $$\surd3 + \surd9 > \surd6 + \surd6$$
If $$a = \frac{\sqrt3 + \sqrt2}{\sqrt3 - \sqrt2}$$ and $$b = \frac{\sqrt3 - \sqrt2}{\sqrt3 + \sqrt2}$$, then what is the value of $$a^2 + b^2 - ab$$?
If the difference between the roots of the equation $$Ax^2 - Bx + C = 0$$ is 4, then which of the following is TRUE?
$$\alpha$$ and $$\beta$$ are the roots of quadratic equation. If $$\alpha + \beta = 8$$ and $$\alpha - \beta = 2\surd5$$, then which of the following equation will have roots $$\alpha^4$$ and $$\beta^4$$?
If $$a$$ and $$b$$ are the roots of the equation $$Px^2 - Qx + R = 0$$, then what is the value of $$\left(\frac{1}{a^2}\right) + \left(\frac{1}{b^2}\right) + \left(\frac{a}{b}\right) + \left(\frac{b}{a}\right)$$?
If $$x^2 - 16x - 59 = 0$$, then what is the value of $$(x - 6)^2 + \left[\frac{1}{(x - 6)^2}\right]$$?
If $$A$$ and $$B$$ are the roots of the equation $$Ax^2 - A^2x + AB = 0$$, then what is the value of $$A$$ and $$B$$ respectively?
$$\alpha$$ and $$\beta$$ are the roots of the quadratic equation $$x^2 - x - 1 = 0$$. What is the value of $$\alpha^2 + \beta^2$$?
If $$a + b + c = 9, ab + bc + ca = 26, a^3 + b^3= 91, b^3 + c^3 = 72$$ and $$c^3 + a^3 = 35$$, then what is the value of $$abc$$?
If $$x^3 - 4x^2 + 19 = 6(x - 1)$$, then what is the value of $$\left[x^2 + \left(\frac{1}{x - 4}\right)\right]$$?
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