GATE CS 2014 Set 1 Q.4 (GA Q.4): Quantitative Aptitude

If $(z + 1/z)^2 = 98$ , compute $(z^2 + 1/z^2)$ .

Your answer

Official answer and solution

Solution

Expand the given square $(z + 1/z)^2$ using the algebraic identity $(a + b)^2 = a^2 + 2ab + b^2$ .

Using the algebraic expansion:

(z + 1/z)^2 = z^2 + 2 \cdot z \cdot \frac{1}{z} + \frac{1}{z^2} = z^2 + 2 + \frac{1}{z^2}

We are given:

(z + 1/z)^2 = 98

Substituting this into the expansion:

z^2 + 2 + \frac{1}{z^2} = 98

z^2 + \frac{1}{z^2} = 98 - 2 = 96

Final answer

Common trap

Forgetting the cross term $+2$ and squaring both sides incorrectly.

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