How to solve question no 23---ALGEBRAIC IDENTITIES Page Number: 49 20. If a + b + c = 0, then a^2/bc + b^2/ca + c^2/ab = (a) 0 (b) 1 (c) -1 (d) 3 21. If a^(1/3) + b^(1/3) + c^(1/3) = 0, then (a) a + b + c = 0 (b) (a + b + c)^3 = 27abc (c) a + b + c = 3abc (d) a^3 + b^3 + c^3 = 0 22. If a + b + c = 9 and ab + bc + ca = 23, then a^3 + b^3 + c^3 - 3abc = (a) 108 (b) 207 (c) 669 (d) 729 23. (a^2 - b^2)^3 + (b^2 - c^2)^3 + (c^2 - a^2)^3 / (a - b)^3 + (b - c)^3 + (c - a)^3 = (a) 3(a + b)(b + c)(c + a) (b) 3(a - b)(b - c)(c - a) (c) (a - b)(b - c)(c - a) (d) (a + b)(b + c)(c + a) 24. The product (a + b)(a - b)(a^2 - ab + b^2)(a^2 + ab + b^2) is equal to (a) a^6 + b^6 (b) a^6 - b^6 (c) a^3 - b^3 (d) a^3 + b^3 25. The product (x^2 - 1)(x^4 + x^2 + 1) is equal to (a) x^8 - 1 (b) x^8 + 1 (c) x^6 - 1 (d) x^6 + 1 26. If a/b + b/a = 1, then a^3 + b^3 = (a) 1 (b) -1 (c) 1/2 (d) 0 27. If 49a^2 - b = (7a + 1/2)(7a - 1/2), then the value of b is (a) 0 (b) 1/4 (c) 1/√2 (d) 1/2 28. One of the factors of (5x + 1)^2 - (5x - 1)^2 is (a) 5 + x (b) 5 - x (c) 5x - 1 (d) 20x 29. If 9x^2 - b = (3x + 1/2)(3x - 1/2), then the value of b is (a) [Content not fully visible] (b) [Content not fully visible] (c) [Content not fully visible] (d) [Content not fully visible]