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MATH / There is a unique pair of positive real numbers satisfying the equations x⁴−6x²y²+y⁴=8 and x³y−xy³=2√(3).Determine x, writing your answer in the form acosθ, with θ in degrees.

Problem

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problem

There is a unique pair of positive real numbers satisfying the equations x4−6x2y2+y4=8andx3y−xy3=23. x^4-6x^2y^2+y^4 = 8 \qquad\mbox{and}\qquad x^3y-xy^3 = 2\sqrt{3}. Determine xx, writing your answer in the form acosθa\cos\theta, with θ\theta in degrees.
Plain-text mathematical notation (without MathML)
There is a unique pair of positive real numbers satisfying the equations x⁴−6x²y²+y⁴=8 and x³y−xy³=2√(3).Determine x, writing your answer in the form acosθ, with θ in degrees.
Original LaTeX notation
There is a unique pair of positive real numbers satisfying the equations \[ x^4-6x^2y^2+y^4 = 8 \qquad\mbox{and}\qquad x^3y-xy^3 = 2\sqrt{3}. \]Determine $x$, writing your answer in the form $a\cos\theta$, with $\theta$ in degrees.

level

Level 4

type

Precalculus

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Source and history

task_id
e9c65e39-ba98-5fb1-92c8-de2506abdb55
task_key
precalculus--test--e9c65e39-ba98-5fb1-92c8-de2506abdb55
task_revision_id
1
config / split
precalculus / test

Official source

initial import