[" 5.Sbow thit."],[" Qy "(3x+7)^(2)-84x=(3x-7)^(2)],[" (v) "(a-b)(a+b)+(b-c)(b+c)+(c-a)(c+a)=0]

Show that. (i) (3x+7)^2-84x=(3x-7)^2 (ii) (9p-5q)^2+180pq=(9p+5q)^2 (iii) (4/3(m)-3/4(n))^2+2mn=16/9(m^2)+9/16(n^2) (iv) (4pq+3q)^2-(4pq-3q)^2=48pq^2 (v) (a-b)(a+b)+(b-c)(b+c)+(c-a)(c+a)=0

If 1176=2^(a)x3^(b)x7^(c), and a,b and c

Show that.(i) (3x+7)2-84x=(3x-7)2( ii) (9p-5q)2+180pq=(9p+5q)2( iii) (43(m)-34(n))2+2mn=169(m2)+916(n2)( iv )(4pq+3q)2-(4pq-3q)2=48pq2(v)(a-b)(a+b)+(b-c)(b+c)+(c-a)(c+a)=0

If 3x=a+b+c, then the value of (x-a)^(3)+(x-b)^(3)+(x-c)^(3)-3(x-a)(x-b)(x-c) is (a) a+b+c( b )(a-b)(b-c)(c-a)(c)0(d) None of these

If 3x=a+b+c , then the value of (x-a)^3+\ (x-b)^3+\ (x-c)^3-3\ (x-a)(x-b)(x-c) is (a) a+b+c (b) (a-b)(b-c)(c-a) (c) 0 (d) None of these

If |(1,1,1),(a,b,c),(a^(3),b^(3),c^(3))| = (a - b) (b - c) (c - a) (a + b + c) , where a,b,c are all different, then the determinant |(1,1,1),((x-a)^(2),(x-b)^(2),(x-c)^(2)),((x-b)(x-c),(x-c)(x-a),(x-a)(x-b))| vanishes when a)a + b + c = 0 b) x = (1)/(3) (a + b + c) c) x = (1)/(2) (a + b + c) d) x = a + b + c

If x^(3)-3x^(2)+3x-7=(x+1)(ax^(2)+bx+c) then a+b+c=4(b)12(c)-10(d)3

If |[1 1 1];[a b c];[ a^3b^3c^3]|=(a-b)(b-c)(c-a)(a+b+c),w h e r ea ,b ,c are different, then the determinant |[1 1 1];[(x-a)^2(x-b)^2(x-c)^2];[(x-b)(x-c) (x-c)(x-a) (x-a)(x-b)| vanishes when a. a+b+c=0 b. x=1/3(a+b+c) c. x=1/2(a+b+c) d. x=a+b+c