1.

If x2+1/x2=27,find the value of 2x-1/x

Answer»

Answer

  • x - ¹/ₓ = ± 5

Given

\bullet \;\; \rm x^2+\dfrac{1}{x^2}=27

To Find

\bullet \;\; \rm x-\dfrac{1}{x}=?

Formula Used

\bullet \;\; \rm (a-b)^2=a^2+b^2-2ab

Solution

\rm x^2+\dfrac{1}{x^2}=27\\\\\implies \rm x^2+\dfrac{1}{x^2}=25+2\\\\\implies \rm x^2+\dfrac{1}{x^2}-2=25\\\\\implies \rm x^2+\bigg(\dfrac{1}{x}\bigg)^2-2.x.\dfrac{1}{x}=25\\\\\rm LHS\ resembles\ formula\ ,a^2+b^2-2ab=(a-b)^2\\\\\implies \rm \bigg(x-\dfrac{1}{x}\bigg)^2=25\\\\\implies \rm x-\dfrac{1}{x}=\pm 5


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