perplexus.info :: Just Math : Smells Trigonometric

Smells Trigonometric (Posted on 2023-11-12)

x and y are real numbers such that, (4x³-3x)²+(4y³-3y)²=1.

Find the maximum of x+y.

No Solution Yet Submitted by Danish Ahmed Khan

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based on Wolfram Alpha

| Comment 2 of 4 |

solve (4x^3-3x)^2+(4y^3-3y)^2=1 for y

typed into Wolfram Alpha gives

y = ± sqrt(1 - x^2)

Then typing

maximum(sqrt(1-x^2)+x)

into Wolfram Alpha gives

max{sqrt(1 - x^2) + x} = sqrt(2) at x = 1/sqrt(2)

Posted by Charlie on 2023-11-12 15:31:22

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