1x+1+2x+25x+4

Related Answers Basic Algebra Question For real numbers,a,b, and,c determine whether each statement is TRUE or FALSE (circle). Edwin drew a scale drawing of a community college. Solve, 1/x+1+2/x+2=5/x+4 - Math - Quadratic Equations.
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1x+1+2x+25x+4. Share with your friends. Solve for x:1/x+1 +2/x+2 =5/x+4 - gvikasyadav509 is waiting for your help. Add your answer and earn points.

If FALSE, justify with an explanation. Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. 1 / x+1 + 2 / x+2 = 5 / x+4 , x is not equal to -1, -2, -4.

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$\\Solution:\\\\ Given: x+\frac1x=5\\\\ \text{Squaring on both sides}\\\\ \Rightarrow (x+\frac1x)^2=5^2\\\\ \Rightarrow x^2+2\times x\times\frac1x+\left (\frac{1}{x} \right )^2=25\ \ \ \ \ \ \ \ [\because (a+b)^2=a^2+b^2+2ab]\\\\ \Rightarrow x^2+2+\frac{1}{x^2}=25\\\\ \Rightarrow x^2+\frac{1}{x^2}=25-2\\\\ \therefore \left (x^2+\frac{1}{x^2} \right )=23\\\\ \text{Squaring on both sides}\\\\ \Rightarrow \left (x^2+\frac{1}{x^2} \right )^2=23^2\\ \Rightarrow x^4+2\times x^2\times\frac1{x^2}+\left (\frac{1}{x^2} \right )^2=529\ \ \ \ \ \ \ \ [\because (a+b)^2=a^2+b^2+2ab]\\\\ \Rightarrow x^4+2+\frac{1}{x^4}=529\\\\ \Rightarrow x^4+\frac{1}{x^4}=529-2\\\\ \therefore \left (x^4+\frac{1}{x^4} \right )=527$

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$\\Solution:\\ Given:\\\\ 4^x-4^{x-1}=24\\\\ \Rightarrow 4^x-\frac{4^x}{4}=24\ \ \ \ [\because a^{m-n}=\frac{a^m}{a^n}]\\\\\\ \Rightarrow 4^x(1-\frac{1}4)=24\\\\\ \Rightarrow 4^x\times\frac34=24\\\\\\ \Rightarrow 4^x=24\times\frac43\\\\\\\ \Rightarrow 4^x=32\\\\\\ \Rightarrow {(2^2)}^x=2^5\\\\ Bases\ are\ equal\ then\ the\ exponents\ are\ also\ equal\\\\ \Rightarrow 2x=5\\\\ \therefore x=\frac52\\\\ Now, \\ (2x)^x={(2\times\frac52)}^\frac52 =5^\frac52=\sqrt{5^5}=\sqrt{5^4\times5}=5^2\sqrt5=25\sqrt5$

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