if-x-x-26-x-5-find-x-5-x-

Question Number 151307 by mathdanisur last updated on 19/Aug/21

if x \sqrt{x} - 26 \sqrt{x} = 5

find x - 5 \sqrt{x} = ?

Answered by MJS_new last updated on 20/Aug/21

x \sqrt{x} - 26 \sqrt{x} - 5 = 0

(\sqrt{x} + 5) (x - 5 \sqrt{x} - 1) = 0

\Rightarrow x - 5 \sqrt{x} = 1

Commented by mathdanisur last updated on 20/Aug/21

Thanmyou Ser

Answered by maged last updated on 20/Aug/21

if x \sqrt{x} - 26 \sqrt{x} = 5

find x - 5 \sqrt{x} = ?

Let : \sqrt{x} = u

u^{3} - 26 u = 5

u^{3} - 26 u - 5 = 0

u^{3} - 25 u - u - 5 = 0

u (u^{2} - 25) - (u + 5) = 0

u (u - 5) (u + 5) - (u + 5) = 0

(u + 5) [(u (u - 5) - 1] = 0

(u + 5) [u^{2} - 5 u - 1] = 0

(\sqrt{x} + 5) (x - 5 \sqrt{x} - 1) = 0

either

\sqrt{x} = - 5 \Rightarrow x = 25

\Rightarrow x - 5 \sqrt{x} = 25 - 5 (- 5) = 25 + 25 = 50

or

x - 5 \sqrt{x} - 1 = 0 \Rightarrow x - 5 \sqrt{x} = 1

Commented by MJS_new last updated on 20/Aug/21

why you solve

26 \sqrt{x} - x \sqrt{x} = 5

when the given equation is

x \sqrt{x} - 26 \sqrt{x} = 5

? ? ?

Commented by mathdanisur last updated on 20/Aug/21

Thankyou Ser

Commented by MJS_new last updated on 20/Aug/21

\sqrt{x} = - 5 has no solution

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