a^(3)+b^(3)+c(a^(2)-ab+b^(2))

If a = (sqrt5 + 1)/(sqrt5 + 1) and b = (sqrt5 -1)/(sqrt5 + 1) , then find the value of (a) (a^(2) + ab + b^(2))/(a^(2) - ab + b^(2)) (b) ((a -b)^(3))/((a + b)^(3)) (c) (3a^(2) + 5ab + b^(2))/(3a^(2) - 5ab + b^(2)) (d) (a^(3) + b^(3))/(a^(3) - b^(3))

Show that |{:(a,b,c),(b,c,a),(c,a,b):}|^2=|{:(2bc-a^(2),c^(2),b^(2)),(c^(2),2ac-b^(2),a^(2)),(b^(2),a^(2),2ab-c^(2)):}|=(a^(3)+b^(3)+c^(3)-3abc)^(2)

The value of the determinant |(bc,ac,ab),(a,b,c),(a^(3),b^(3),c^(3))| is a)(a + b + c) b)a + b + c -ab c) (a^(2) - b^(2))(b^(2) - c^(2)) (c^(2) - a^(2)) d) a^2+b^2+c^2

The product (a+b)(a-b)(a^(2)-ab+b^(2))(a^(2)+ab+b^(2)) is equal to: a^(6)+b^(6)(b)a^(6)-b^(6)(c)a^(3)-b^(3)(d)a^(3)+b^(3)

If a, b, c and d are in proportion, then show that (a^(3)+3ab^(2))/(3a^(2)b+b^(3))=(c^(3)+3cd^(2))/(3c^(2)d+d^(3))

If a+b+c=0, then which of the following are correct? 1. a^(3) + b^(3) + c^(3) = 3abc 2. a^(2) + b^(2) + c^(2) = -2(ab + bc + ca) 3. a^(3) + b^(3) + c^(3) = -3ab(a+b) Select the correct answer using the code given below

a^(2)b^(3)x2ab^(2) is equal to: 2a^(3)b^(4)(b)2a^(3)b^(5)(c)2ab (d) a^(3)b^(5)

If a:b=2:3, then the value of (5a^(3)-2a^(2)b):(3ab^(2)-b^(3)) is :

Simplify the following: (6) (i) (a^(3)b^(2)c-ab^(3)c)-(3abc^(3)-a^(3)b^(2)c)-(4ab^(3)c+2abc^(3))