The statement "R is numerically equal to the square of the reactance X" simply means `R = X^2`.
Recall (from Application of Complex Numbers) that
In this case, from the definition, and to make life easier, we assume that XL − XC = X.
Now, on squaring both sides, we have
R2 + X2 = 4
But R = X2 (since R is equal to the square of X) so
R2 + R = 4
R2 + R − 4 = 0
Using quadratic formula gives
Only the positive root has meaning (since we cannot have negative resistance), so
R = 1.56 Ω. and therefore X = √1.56 = 1.25 Ω.
In this question, the 2 interssecting functions are a parabola (`X = R^2 + R - 4`) and a straight line (`X=4`). In the graph, we can see the 2 solutions we obtained, one is negative (`R=-2.56`) and the other one is positive, at (`R=1.56`).
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