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

$$\mathrm{if}\mathrm{x}\sqrt{\mathrm{x}}-26\sqrt{\mathrm{x}}=5$$$$\mathrm{find}\mathrm{x}-5\sqrt{\mathrm{x}}=?$$

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

$$\mathrm{Thanmyou}\mathrm{Ser}$$

Answered by maged last updated on 20/Aug/21

$$$$$$\mathrm{if}\mathrm{x}\sqrt{\mathrm{x}}-26\sqrt{\mathrm{x}}=5$$$$\mathrm{find}\mathrm{x}-5\sqrt{\mathrm{x}}=?$$$$\mathrm{Let}:\sqrt{\mathrm{x}}=\mathrm{u}$$$${\mathrm{u}}^3-26\mathrm{u}=5$$$${\mathrm{u}}^3-26\mathrm{u}-5=0$$$${\mathrm{u}}^3-25\mathrm{u}-\mathrm{u}-5=0$$$$\mathrm{u}({\mathrm{u}}^2-25)-(\mathrm{u}+5)=0$$$$\mathrm{u}(\mathrm{u}-5)(\mathrm{u}+5)-(\mathrm{u}+5)=0$$$$(\mathrm{u}+5)[(\mathrm{u}(\mathrm{u}-5)-1]=0$$$$(\mathrm{u}+5)[{\mathrm{u}}^2-5\mathrm{u}-1]=0$$$$(\sqrt{\mathrm{x}}+5)(\mathrm{x}-5\sqrt{\mathrm{x}}-1)=0$$$$\mathrm{either}$$$$\sqrt{\mathrm{x}}=-5\Rightarrow \mathrm{x}=25$$$$\Rightarrow \mathrm{x}-5\sqrt{\mathrm{x}}=25-5(-5)=25+25=50$$$$\mathrm{or}$$$$\mathrm{x}-5\sqrt{\mathrm{x}}-1=0\Rightarrow \mathrm{x}-5\sqrt{\mathrm{x}}=1$$$$$$

Commented by MJS_new last updated on 20/Aug/21

$$\mathrm{why}\mathrm{you}\mathrm{solve}$$$$26\sqrt{x}-x\sqrt{x}=5$$$$\mathrm{when}\mathrm{the}\mathrm{given}\mathrm{equation}\mathrm{is}$$$$x\sqrt{x}-26\sqrt{x}=5$$$$???$$

Commented by mathdanisur last updated on 20/Aug/21

$$\mathrm{Thankyou}\mathrm{Ser}$$

Commented by MJS_new last updated on 20/Aug/21

$$\sqrt{x}=-5\mathrm{has}\mathrm{no}\mathrm{solution}$$

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