Question

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

Answer 1

Answer:

x^2+1=27x^2

1=26x^2

26x=1

x=1/26

2x-1/x

=2×1/26-1/1/26

=2/26-1/26

=1/26

Answer 2

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

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