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Nilabhro

Sep 29, 2013

If x + 1/x = 5 then X4 + 1/X4= ?

IF X + 1/X=3 THEN X4 + X4= ?

Answers(2)

Answer

Parthasaradhi M

Member since Apr 1, 2017

\\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                                               \\Solution:\\\\ Given: x+\frac1x=3\\\\ \text{Squaring on both sides}\\\\ \Rightarrow (x+\frac1x)^2=3^2\\\\ \Rightarrow x^2+2\times x\times\frac1x+\left (\frac{1}{x} \right )^2=9\ \ \ \ \ \ \ \ [\because (a+b)^2=a^2+b^2+2ab]\\\\ \Rightarrow x^2+2+\frac{1}{x^2}=9\\\\ \Rightarrow x^2+\frac{1}{x^2}=9-2\\\\ \therefore \left (x^2+\frac{1}{x^2} \right )=7\\\\ \text{Squaring on both sides}\\\\ \Rightarrow \left (x^2+\frac{1}{x^2} \right )^2=7^2\\ \Rightarrow x^4+2\times x^2\times\frac1{x^2}+\left (\frac{1}{x^2} \right )^2=49\ \ \ \ \ \ \ \ [\because (a+b)^2=a^2+b^2+2ab]\\\\ \Rightarrow x^4+2+\frac{1}{x^4}=49\\\\ \Rightarrow x^4+\frac{1}{x^4}=49-2\\\\ \therefore \left (x^4+\frac{1}{x^4} \right )=47

Kishore Kumar


Squaring on both the sides, we get

Squaring on both the sides again, we get
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