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Question-136344




Question Number 136344 by Gideon last updated on 21/Mar/21
Commented by mindispower last updated on 21/Mar/21
x^2 +6x=(x+3)^2 −9  t=(x+3)^2   (5/( (√(t−1))))+(1/( (√(t−4))))=(4/t)  we have t>4,t−1>3⇒(√(t−1))<t⇔  (5/( (√(t−1))))>(4/( (√(t−1))))>(4/t)   no solution over R
$${x}^{\mathrm{2}} +\mathrm{6}{x}=\left({x}+\mathrm{3}\right)^{\mathrm{2}} −\mathrm{9} \\ $$$${t}=\left({x}+\mathrm{3}\right)^{\mathrm{2}} \\ $$$$\frac{\mathrm{5}}{\:\sqrt{{t}−\mathrm{1}}}+\frac{\mathrm{1}}{\:\sqrt{{t}−\mathrm{4}}}=\frac{\mathrm{4}}{{t}} \\ $$$${we}\:{have}\:{t}>\mathrm{4},{t}−\mathrm{1}>\mathrm{3}\Rightarrow\sqrt{{t}−\mathrm{1}}<{t}\Leftrightarrow \\ $$$$\frac{\mathrm{5}}{\:\sqrt{{t}−\mathrm{1}}}>\frac{\mathrm{4}}{\:\sqrt{{t}−\mathrm{1}}}>\frac{\mathrm{4}}{{t}}\: \\ $$$${no}\:{solution}\:{over}\:\mathbb{R} \\ $$$$ \\ $$

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