Question
If x + 1/x = 3 (x ≠0), find the value of x³ +
1/x³.Solution
(x + 1/x)² = x² + 1/x² + 2 = 3² = 9 ⇒ x² + 1/x² = 9 − 2 = 7 Now use identity: x³ + 1/x³ = (x + 1/x)(x² + 1/x² − 1) = 3 × (7 − 1) = 3 × 6 = 18.
If 64x3 - 343y3 = (4x - Ay) X (Bx2 + 49y2 + Cxy), then find the value of 3 X (2A + 6B) - 2C.
If a + b + c = 8, a² + b² + c² = 18 and ab + b c+ ca = 12, then what is the value of a³ + b³ +c³ –3abc?
If Â
 = 4 then 
 (a + 7)2 + (b – 2) 2 + (c + 3) 2 = 0, then find the value of 3a - 2b + c.
Two positive numbers differ by 2, and the sum of their reciprocals is 3/4. What is the larger number?
(x + 1)2 + (y – 3) 2 + (z + 5) 2 = 0, then find the value of 2x + 3y - z.
If x + 1/x = 5, then x2 + 1/x2 is:
(x – 6) 2 + (y + 2) 2 + (z – 4) 2 = 0, then find the value of 4x - 3y + z.
22% of ‘x’ is equal to 66% of ‘y’, then find the value of x: y.
