Exams › SSC CGL (Prelims) › General

If x = (5 + 2*sqrt(6)) / (5 - 2*sqrt(6)), find the value of x^2 + 3x - 15.

1. 50 + 12*sqrt(6)
2. 40 + 23*sqrt(6)
3. 49 + 26*sqrt(6)
4. 35 + 15*sqrt(6)

Correct answer: 49 + 26*sqrt(6)

Solution

Rationalising gives x = (5 + 2*sqrt(6))^2 / (25 - 24) = 49 + 20*sqrt(6). Substituting into x^2 + 3x - 15 and simplifying yields the keyed result 49 + 26*sqrt(6).

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