If `sqrt(alpha_1-1)+2sqrt(alpha_2-4)+3sqrt(alpha_3-9)+4sqrt(alpha_4-16)=(alpha_1+alpha_2+alpha_3+alpha_4)/2w h e r ealpha_1,alpha_2,alpha_3,alpha_4` are all real. Thena. `alpha_1+alpha_2=10` b. `alpha_2+alpha_3=26` c. `alpha_4-alpha_3=12` d. `alpha_4-alpha_2-alpha_1=22`

if sqrt(alpha_(1)-1)+2sqrt(alpha_(2)-4)+3sqrt(alpha_(3)-9)+4sqrt(alpha_(4)-16)=(alpha_(1)+alpha_(2)+alpha_(3)+alpha_(4))/(2) where alpha_(1),alpha_(2),alpha_(3),alpha_(4) are all real. Then

If the roots of equation x^3+a x^2+b=0a r ealpha_1,alpha_2 and alpha_3(a ,b!=0) , then find the equation whose roots are (alpha_1alpha_2+alpha_2alpha_3)/(alpha_1alpha_2alpha_3),(alpha_2alpha_3+alpha_3alpha_1)/(alpha_1alpha_2alpha_3),(alpha_1alpha_3+alpha_1alpha_2)/(alpha_1alpha_2alpha_3)

If alpha_1, ,alpha_2, ,alpha_n are the roots of equation x^n+n a x-b=0, show that (alpha_1-alpha_2)(alpha_1-alpha_3)(alpha_1-alpha_n)=n(alpha_1^ n-1+a)

Prove that |1alphaalpha^2alphaalpha^2 1alpha^2 1alpha|=-(1-alpha^3)^2dot

If the roots of equation x^(3) + ax^(2) + b = 0 are alpha _(1), alpha_(2), and alpha_(3) (a , b ne 0) . Then find the equation whose roots are (alpha_(1)alpha_(2)+alpha_(2)alpha_(3))/(alpha_(1)alpha_(2)alpha_(3)), (alpha_(2)alpha_(3)+alpha_(3)alpha_(1))/(alpha_(1)alpha_(2)alpha_(3)), (alpha_(1)alpha_(3)+alpha_(1)alpha_(2))/(alpha_(1)alpha_(2)alpha_(3)) .

prove that : tan(alpha)+2 tan(2alpha) +4(tan4alpha)+8cot(8alpha) = cot(alpha)

If alpha_r=(cos2rpi+isin2rpi)^(1/10) , then |(alpha_1, alpha_2, alpha_4),(alpha_2, alpha_3, alpha_5),(alpha_3, alpha_4, alpha_6)|= (A) alpha_5 (B) alpha_7 (C) 0 (D) none of these

Suppose a sample space S consists of 4 elements, i.e., S={alpha_1, alpha_2, alpha_3, alpha_4} " where " alpha_1, alpha_2, alpha_3, alpha_4 are pair wise mutually exclusive. Which function defines a probability function on S? (1) P(alpha_1)=1/2, P(alpha_2)=1/3, P(alpha_3)=1/4, P(alpha_4)=1/4 (2) P(alpha_1)=1/4, P(alpha_2)=-1/2, P(alpha_3)=7/9, P(alpha_4)=1/3 (3) P(alpha_1)=1/2, P(alpha_2)=1/4, P(alpha_3)=1/8, P(alpha_4)=1/8 (4) P(alpha_1)=1/2, P(alpha_2)=1/4, P(alpha_3)=1/8, P(alpha_4)=0

If cot^3alpha+cot^2alpha+cotalpha=1 then (a) cos2alpha.tanalpha=-1 (b) cos2alpha.tanalpha=1 (c) cos2alpha-tan2alpha=1 (d) cos2alpha-tan2alpha=-1

If sum_(n=1)^nalpha_n=a n^2+b n ,w h e r ea ,b are constants and alpha_1,alpha_2,alpha_3 in {1,2,3,......,9}a n d25alpha_1,37alpha_2,49alpha_3 be three digit number, then prove that |alpha_1alpha_2alpha_3 5 7 9 25alpha_1 37alpha_2 49alpha_3|=0