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1

IIT-JEE 1986

Subjective
For $$a \le 0,$$ determine all real roots of the equation $$${x^2} - 2a\left| {x - a} \right| - 3{a^2} = 0$$$

Answer

$$\left\{ {a \pm a\sqrt 2 ,\,\, - a \pm a\sqrt 6 } \right\}$$
2

IIT-JEE 1985

Subjective
Solve for $$x$$ ; $${\left( {5 + 2\sqrt 6 } \right)^{{x^2} - 3}} + {\left( {5 - 2\sqrt 6 } \right)^{{x^2} - 3}} = 10$$

Answer

$$ \pm 2,\, \pm \sqrt 2 $$
3

IIT-JEE 1983

Subjective
Find all real values of $$x$$ which satisfy $${x^2} - 3x + 2 > 0$$ and $${x^2} - 2x - 4 \le 0$$

Answer

$$\left[ { - 1,1} \right) \cup \left( {2,4} \right]$$
4

IIT-JEE 1983

Subjective
If one root of the quadratic equation $$a{x^2} + bx + c = 0$$ is equal to the $$n$$-th power of the other, then show that $$${\left( {a{c^n}} \right)^{{1 \over {n + 1}}}} + {\left( {{a^n}c} \right)^{{1 \over {n + 1}}}} + b = 0$$$

Answer

Solve it.

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