If-x-2-65x-64-x-then-x-x-

Question Number 194226 by BaliramKumar last updated on 30/Jun/23

If x^{2} - 65 x = 64 \sqrt{x} then \sqrt{x - \sqrt{x}} = ?

Answered by Frix last updated on 30/Jun/23

x^{2} - 65 x = 64 \sqrt{x}

x = 0 \Rightarrow \sqrt{x - \sqrt{x}} = 0 ★

x^{\frac{3}{2}} - 65 \sqrt{x} - 64 = 0

x = t^{2} \land t > 0

t^{3} - 65 t - 64 = 0

(t + 1) (t^{2} - t - 64) = 0

t = \frac{1 + \sqrt{257}}{2} = \sqrt{x}

x = \frac{129 + \sqrt{257}}{2}

\Rightarrow \sqrt{x - \sqrt{x}} = 8 ★

Answered by Frix last updated on 30/Jun/23

x^{2} - 65 x - 64 \sqrt{x} = 0

\sqrt{x} (\sqrt{x} + 1) (x - \sqrt{x} - 64) = 0

x = 0 ★

\sqrt{x - \sqrt{x}} = 0

x - \sqrt{x} - 64 = 0

x - \sqrt{x} = 64

\sqrt{x - \sqrt{x}} = 8 ★

Answered by manxsol last updated on 30/Jun/23

x^{2} - x = 64 (x + \sqrt{x})

{(\sqrt{x})}^{4} - {(\sqrt{x})}^{2} = 64 (x + \sqrt{x})

(\sqrt{x}^{2} - \sqrt{x}) (\sqrt{x}^{2} + \sqrt{x}) = 64 (x + \sqrt{x})

(x - \sqrt{x}) (x + \sqrt{x}) = 64 (x + \sqrt{x})

x - \sqrt{x} = 64

\sqrt{x - \sqrt{x}} = 8 s o l I

x + \sqrt{x} = 0

\sqrt{x} (\sqrt{x} + 1) = 0

x = 0 \sqrt{x - \sqrt{x}} = 0 s o l I I

\sqrt{x} = - 1 \times

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