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NEST2026MathematicsQuadratic Equation

A possible solution of the system of equations x^2 - 8xy + 16y^2 = 0 ( ₁₀ x)^2 + 2( ₁₀ x)( ₁₀ y) + ( ₁₀ y)^2 = 4 is

Options

  1. Ax = 1 5 , y = 1 20
  2. Bx = 100, y = 25
  3. Cx = 40, y = 10
  4. Dx = 4 25 , y = 1 16

Correct answer

A. x = 1 5 , y = 1 20

Step-by-step solution

The first equation is x^2 - 8xy + 16y^2 = 0 (x - 4y)^2 = 0 x = 4y The second equation is ( ₁₀ x)^2 + 2( ₁₀ x)( ₁₀ y) + ( ₁₀ y)^2 = 4 ( ₁₀ x + ₁₀ y)^2 = 4 ₁₀ (xy) = 2 xy = 10^2 = 100 or xy = 10⁻² = 1 100 Substituting x = 4y into xy = 100 gives 4y^2 = 100 y^2 = 25 . Since y > 0 , y = 5 and x = 20 . Substituting x = 4y into xy = 1 100 gives 4y^2 = 1 100 y^2 = 1 400 . Since y > 0 , y = 1 20 and x = 1 5 . Therefore, a possible solution is x = 1 5 , y = 1 20 . Answer: x = 1 5 , y = 1 20

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