[" DIf mopootion "*" is delined by "^(2)b=2^(2)+b^(2)],[" then "(1^(*)2)^(*)*5^(8)=?]

If a,b,c are real numbers such that a+b+c=0 and a^(2)+b^(2)+c^(2)=1, then (3a+5b-8c)^(2)+(-8a+3b+5c)^(2)+(5a-8b+3c)^(2) is equal to

(-8b^(2)+4b-8)+(-2b^(2)-5b-1)

If (4b^(2)+(1)/(b^(2)))=2, then (8b^(3)+(1)/(b^(3)))=? (a) 0 (b) 1 (c) 2 (d) 5

If (a+b):(a-b)=1:5 then (a^2-b^2):(a^2+b^2)=

Show that the following points are collinear: (i) A(2, -2), B(-3, 8) and C(-1, 4) (ii) A(-5, 1), B(5, 5) and C(10, 7) (iii) A(5, 1), B(1, -1) and C(11, 4) (iv) A(8, 1), B(3, -4) and C(2, -5)

, (a+b)^2 + (a-b)^2 = 2(a^2 + b^2) or (a+b)^2 - (a -b)^2= 4ab or ab = (frac(a+b)(2))^2 -(frac(a-b)(2))^2 to find the following. Let's find 8xy( x^2 + y^2 ) when (x+y) = 5 and (x-y) = 1