If x + y = 3, then what is the value of x3 + y3 + 9xy?
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If x2 – 4x + 1 = 0, then what is the value of x9 + x7 – 194x5 – 194x3?
If [a + (1/a)]2 – 2[a – (1/a)] = 12, then which of the following is a value of 'a'?
If x = (a/b) + (b/a), y = (b/c) + (c/b) and z = (c/a) + (a/c), then what is the value of xyz – x2 – y2 – z2?
A root of equation ax2 + bx + c = 0 (where a, b and c are rational numbers) is 5 + 3√3. What is the value of (a2 + b2 + c2)/(a + b + c)?
If x = (√5) + 1 and y = (√5) – 1, then what is the value of (x2/y2) + (y2/x2) + 4[(x/y) + (y/x)] + 6?
If P = 7 + 4√3 and PQ = 1, then what is the value of (1/P2) + (1/Q2)?
Which of the following statement(s) is/are true?
I. (65)1/6 > (17)1/4 > (12)1/3 II. (17)1/4 > (65)1/6 > (12)1/3 III. (12)1/3 > (17)1/4 > (65)1/6
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