Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
COMEDK2025MathematicsTrigonometric Ratios & IdentitiesActual

If x+ ^2 x=1 then ^8 x+2 ^6 x+ ^4 x is equal to

Options

  1. A0
  2. B1
  3. C-1
  4. D2

Correct answer

B. 1

Step-by-step solution

Given x + ² x = 1 . This implies x = 1 - ² x = ² x . We need to evaluate ⁸ x + 2 ⁶ x + ⁴ x . Substituting ² x = x , we get: ( ² x)⁴ + 2( ² x)³ + ( ² x)² = ( x)⁴ + 2( x)³ + ( x)² . Factoring the expression, we have ( ² x + x)² . Since x + ² x = 1 , the expression becomes (1)² = 1 . Answer: 1

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 COMEDK PYQs