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Question Number 56481 by Gulay last updated on 17/Mar/19

Commented by Gulay last updated on 17/Mar/19

$$\mathrm{sir}\mathrm{plz}\mathrm{help}\mathrm{me}$$$$$$

Answered by tanmay.chaudhury50@gmail.com last updated on 17/Mar/19

$$(3-a)-\sqrt{{(a-4)}^2}$$$$3-a-(a-4)$$$$3-a-a+4\to 7-2a$$

Commented by Gulay last updated on 17/Mar/19

$$\mathrm{thanks}\mathrm{sir}$$

Commented by 121194 last updated on 17/Mar/19

$$(3-a)-\mid a-4\mid$$$$a>4$$$$(3-a)-(a-4)=7-2a$$$$a<4$$$$(3-a)+(a-4)=-1$$

Commented by tanmay.chaudhury50@gmail.com last updated on 17/Mar/19

Commented by tanmay.chaudhury50@gmail.com last updated on 17/Mar/19

Answered by kaivan.ahmadi last updated on 17/Mar/19

$$let$$$$f\left(a\right)={\left(\sqrt{3-a}\right)}^2-\sqrt{a^2-8a+16}\Rightarrow$$$$f\left(a\right)={\left(\sqrt{3-a}\right)}^2-\sqrt{{(a-4)}^2}=$$$${\left(\sqrt{3-a}\right)}^2-\mid a-4\mid$$$$D_f=\{a\mid 3-a⩾0\}=\{a\mid a⩽3\}$$$$\Rightarrow a-4⩽-1\Rightarrow \mid a-4\mid =4-a$$$$\Rightarrow f\left(a\right)=3-a-(4-a)=-1$$$$$$

Commented by tanmay.chaudhury50@gmail.com last updated on 17/Mar/19

Commented by tanmay.chaudhury50@gmail.com last updated on 17/Mar/19

Commented by 121194 last updated on 18/Mar/19

$${\left(\sqrt{-1}\right)}^2=i^2=-1$$$$\sqrt{{(-1)}^2}=\sqrt{1}=1=\mid -1\mid$$

Commented by MJS last updated on 19/Mar/19

$$\sqrt[n]{x}\mathrm{always}\mathrm{means}\mathrm{the}\mathrm{principal}\mathrm{value}$$$$\mathrm{we}{\mathrm{don}}^{\prime }\mathrm{t}\mathrm{solve}\mathrm{for}\mathrm{anything}\mathrm{writing}$$$$4+\sqrt{2},\sqrt[3]{3}-\sqrt[6]{5}\mathrm{i},...$$$$\mathrm{solving},\mathrm{we}\mathrm{look}\mathrm{for}allpossible\mathrm{values}:$$$$\sqrt{x}=3\Rightarrow x=9\mathrm{without}\mathrm{any}\mathrm{doubt}\mathrm{for}x\in \mathbb{C}$$$$\mathrm{also}\sqrt[3]{-x}=2\Rightarrow x=-8$$$$y=-\sqrt{5}\Rightarrow \mathrm{nothing}\mathrm{to}\mathrm{solve}$$$$\mathrm{but}$$$$z^2=7\Rightarrow z=-\sqrt{7}\vee z=\sqrt{7}$$$$z^3=11\Rightarrow z=\sqrt[3]{11}\vee z=-\sqrt[3]{11}(\frac{1}{2}-\frac{\sqrt{3}}{2}\mathrm{i})\vee z=-\sqrt[3]{11}(\frac{1}{2}+\frac{\sqrt{3}}{2}\mathrm{i})$$$$$$$$-\sqrt{x};\sqrt{x}\mathrm{with}x\in {\mathbb{R}}^{+}\mathrm{are}\mathrm{just}\mathrm{rational}\mathrm{numbers}$$$$\mathrm{it}\mathrm{makes}\mathrm{no}\mathrm{sense}\mathrm{to}\mathrm{see}‘‘2-{\sqrt{3}}^{″}\mathrm{as}2\mathrm{different}$$$$\mathrm{numbers}...\mathrm{you}\mathrm{also}{\mathrm{don}}^{\prime }\mathrm{t}\mathrm{see}‘‘-3^{″}\mathrm{when}$$$$‘‘3^{″}\mathrm{is}\mathrm{written}.$$

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