Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
KVPY2016MathematicsSequences and Series

The number of triples (x, y, z) of real numbers satisfying the equation x⁴+y⁴+z⁴+1=4 x y z is

Options

  1. A0
  2. B4
  3. C8
  4. Dmore than 8

Correct answer

B. 4

Step-by-step solution

(x, y, z) are real & x⁴, y⁴, z⁴ are positive real numbers array l x⁴+y⁴+z⁴+1 4 |x y z| (x y z) |x y z| i.e., x y z>0 array So it holds equality x ⁴= y ⁴= z ⁴=1 ; But xyz >0 ( x , y , z ) (1,1,1),(1,-1,-1),(-1,1,-1),(-1,-1,1) So no. of triplets is 4 .

Practice Sequences and Series on Quantrex Academy →

More from Sequences and Series

Every term of a geometric progression is positive , and every term is the sum of the two preceding terms. Then the common ratio of the geometric progression is: 2026If k is the arithmetic mean of two given quantities and p, q are the geometric means between the same two quantities, then p^3 + q^3 is: 2026Let ' a ' and ' b ' be two numbers where a < b . The geometric mean of these numbers exceeds the smaller number by 12 and the arithmetic mean is smaller than the larger number by 2 2026The product of three numbers in geometric progression is 8 and the sum of the product of the numbers taken in pairs is 14. Find the numbers. 2026Let a₁, a₂, a₃, be a geometric progression of positive integers such that a₁ = 3 and a_ n+2 - 2a_n = a_ n+1 for all positive integers n . What is the value of a₁ + a₂ + a₃ + a₄ + a 2026The angles of a triangle are in A.P and the greatest angle is double the least angle, then sine of the third angle is 2026If we insert two numbers between 2 and 4 so that the resulting sequence is in G.P, then the inserted numbers in the order are 2026If S _ n =1^3+2^3+ . .+ n ^3 and T _ n =1+2+ . .+ n , then 2025 Full Sequences and Series list All KVPY PYQs