Предмет: Алгебра, автор: frankbrown

If n³ = x and n² = 20x, where n > 0, what is the value of x? ​

Ответы

Автор ответа: d3782741
0

n^2 = 20x\implies |n| = \sqrt{20x}

As n > 0 the previous equation is equivalent to n=\sqrt{20x} with the condition that x > 0.

Plugging that into n^3 = x we have

20^{3/2}\cdot x^{3/2} = x\iff x\cdot\Big(20^{3/2}\sqrt{x}-1\Big) = 0, where x > 0.

Therefore,

20^{3/2}\cdot\sqrt{x} - 1 = 0 \iff \sqrt{x} = 20^{-3/2} \iff x = 20^{-3}.

Ans. x=20^{-3} = 0.000125

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