Algebraic Identities

13 lessons · 36 questions · 4 PYQs

What the exams ask here

x+1/x=3 find x^3+1/x^3
a+b+c=0 then a^3+b^3+c^3
simplify big expression
a + b + c = 0 with decimals: sum of a^2/(bc) = 3 (JIPMAT 2025 Q15)
x^3 + y^3 = 468, x + y = 12 -> x^4 + y^4 (JIPMAT 2025 Q19)
a + b = 2c -> a/(a - c) + b/(b - c) (JIPMAT 2025 Q29)
(x^2 + y^2)/xy = k unchanged when x -> x + y, y -> |x - y| (Indore 2026 MCQ Q19, memory-based)
a^2 + b^2 + c^2 + 2a - 2b - 2c + 3 = 0 -> a + b + c
x + y + z = 12, x^2 + y^2 + z^2 = 44 -> xy + yz + zx; a^3 + b^3 + c^3 - 3abc for 2023, 2024, 2025
4x^2 + 9y^2 = 12xy -> x : y
x = cbrt(2 + sqrt3) + cbrt(2 - sqrt3) -> x^3 - 3x
(x - 1)(x + 1)(x^2 + 1)...(x^128 + 1)
factors of a^4 + a^2 + 1, x^4 + 4