If `f(x)=(a_1x+b_1)^2+(a_2x+b_2)^2+...+(a_n x+b_n)^2` , then prove that `(a_1b_1+a_2b_2++a_n b_n)^2lt=(a1 2+a2 2++a n2)^(b1 2+b2 2++b n2)dot`

If f(x)=(a_1x+b_1)^2+(a_2x+b_2)^2+...+(a_n x+b_n)^2 , then prove that (a_1b_1+a_2b_2+...+a_n b_n)^2lt=(a_1^ 2+a_2^ 2+...+a_ n^2)(b_1^ 2+b_2^ 2+..+b_ n^2)dot

If f(x)=(a_1x+b_1)^2+(a_2x+b_2)^2+...+(a_n x+b_n)^2 , then prove that (a_1b_1+a_2b_2+...+a_n b_n)^2lt=(a_1^ 2+a_2^ 2+...+a_ n^2)(b_1^ 2+b_2^ 2+..+b_ n^2)dot

If f(x)=(a_(1)x+b_(1))^(2)+(a_(2)x+b_(2))^(2)+...+(a_(n)x+b_(n))^(2), then prove that (a_(1)b_(1)+a_(2)b_(2)+...+a_(n)b_(n))^(2)<=(a_(1)^(2)+a_(2)^(2)+...+a_(n)^(2))(b_(1)^(2)+b_(2)^(2)+...+b_(n)^(2))

If (a_1+ib_1)(a_2+ib_2)...(a_n+ib_n) = x+iy , prove that : (a_1^2+b_1^2)(a_2^2+b_2^2)...(a_n^2+b_n^2)=x^2+y^2 .

If (a_1+ib_1)(a_2+ib_2).......(a_n+ib_n)=A+iB, " then " (a_1^2+b_1^2)(a_2^2+b_2^2).....(a_n^2+b_n^2)=

Prove by vector method that (a_1b_1+a_2b_2+a_3b_3)^2lt+(a_1^2+a_2^2+a_3^2)(b_1^2+b_2^2+b_3^2)

If (1 + x +x^2)^n = a_0 +a_1x + a_2x^2 + ….+a_(2n)x^(2n) then prove that a_0 +a_1 +a_2 + ……a_(2n) = 3^n

If the oints (a_1b_1),(a_2b_2) and (a_1-a_2,b_1-b_2) are collinear, then show that a_1b_2=a_2b_1

If (1+x+x^(2))^(n)=b_(0)+b_(1)x+b_(2)x^(2)+….+b_(2n)x^(2n) then prove that b_(0)-b_(1)+b_(2)-….+b_(2n)=1

If (1+x+x^(2))^(n)=b_(0)+b_(1)x+b_(2)x^(2)+….+b_(2n)x^(2n) then prove that b_(0) +b_(1)+b_(2)+…+b_(2n)=3^(n)