Question

if x-1/x=5,then find the value of x²+1/x²​

Answer 1

the answer is 27

hope it helps you::))

Answer 2

$\rm{x-\dfrac{1}{x}=5}$

• Squaring On Both Sides

$\to\rm{\left(x-\dfrac{1}{x}\right)^2=5^2}$

• Apply Algebraic Identity : $\rm{(a-b)^2=a^2+b^2-2ab}$

$\to\rm{x^2+\dfrac{1^2}{x^2}-2\times x\times \dfrac{1}{x}=5^2}$

$\to\rm{x^2+\dfrac{1^2}{x^2}-2=5^2}$

• We Know 5² = 25

$\to\rm{x^2+\dfrac{1^2}{x^2}-2=25}$

• Adding 2 to Both Sides

$\to\rm{x^2+\dfrac{1^2}{x^2}-2+2=25+2}$

$\to\rm{x^2+\dfrac{1^2}{x^2}=27}$