Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET2013MathematicsTrigonometric Ratios & Identities

If + =p and ^3 + ^3 =q , then p (p^2-3 ) is equal to

Options

  1. Aq
  2. B2 q
  3. C-q
  4. D-2 q

Correct answer

D. -2 q

Step-by-step solution

aligned & Given, + =p & and ^3 + ^3 =q & ( + ) & ( ^2 - + ^2 )=q aligned p(1- )=q [From Eq. (i) and ^2 + ^2 =1 ] aligned & 1- = q p & =1- q p aligned On squaring both sides of Eq. (i), we get aligned & ^2 + ^2 +2 =p^2 & 1+2 (1- q p )=p^2 [from Eq. (iii)] & p+2(p-q)=p^3 & 3 p-2 q=p^3 & p^3-3 p=-2 q & p (p^2-3 )=-2 q & aligned

Practice Trigonometric Ratios & Identities on Quantrex Academy →

More from Trigonometric Ratios & Identities

If x+ x= 1 2 and 0 < x < , then x= 2025If A and B are acute angles satisfying 3 ^2 A+2 ^2 B=4 and 3 A B = 2 B A , then A+2 B= 2025In a ABC , if ^2 ~B = A and 2 ^2 ~A =3 ^2 ~B , then the triangle is 202512 2 12 3 12 4 12 5 12 6 12 = 2025If ( 4 + )= ^3 ( 4 + ) , then ( + ) ( - )= 2025If A+B+C+D=2 , then A+ B+ C+ D= 2025(4 ^2 20 -1 ) (4 ^2 3 20 -1 ) (4 ^2 5 20 +1 ) (4 ^2 7 20 -1 ) (4 ^2 9 20 -1 )= 2025If A and B are the values such that (A+B) and (A-B) are not odd multiples of 2 and 2 (A+B)=3 (A-B) , then A A= 2025 Full Trigonometric Ratios & Identities list All AP EAMCET PYQs